Bài 1: Chứng minh răng :

a ) ( 2006n +2 )  ⋮${\displaystyle ⋮}$ 2 ( với mọi n la số tự nhiên )
b ) 15⁵ + 15⁶  ⋮${\displaystyle ⋮}$ 16

tìm x ∈ Z biết : a, ( x - 1) * ( x - 2 ) * ( 5 - x ) < 0 b , 9(x&#x2212;1)2" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:22.5px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">(x−1)2$(x-1{)}^2$ + 8(y&#x2212;1)2" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:22.5px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">(y−1)2$(y-1{)}^2$ = 25 c , 3()8" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:22.5px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">x−5)8$x-5{)}^8$ = 27()3" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:22.5px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">x−5)3$x-5{)}^3$ d , 16 ( x - 5)^3 = (x - 5)^5

Tìm x ;y để : 3.2" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:23.4px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">x2$x^2$.y + 5. 2" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:23.4px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">x2$x^2$ + 3. 2" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:23.4px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">y2$y^2$ + 5.y = 16

tìm x ; y biết : 2.2" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:23.4px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">x2$x^2$.y + 3.x.y +2.x.2" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:23.4px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">y2$y^2$ + 3.2" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:23.4px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">y2$y^2$ = 10

Cho tam giác $ABC$ có tâm ngoại tiếp $O$ và tâm đường tròn $Euler$ là $N.D,E,F$ lần lượt là hình chiếu của $N$ lên $BC,CA,AB.M$ là trung điểm $ON.MD,ME,MF$ cắt $EF,FD,DE$ lần lượt tại $X,Y,Z$. Gọi $P,Q,R$ lần lượt là trung điểm $BC,CA,AB.U,V,W$ lần lượt là trung điểm $AP,BQ,CR$.

Chứng minh rằng $XU,YV,ZW$ đồng quy.

a) (x - 6)² = 9

b) 35 - 3.|x| = (2³ - 4)

c) |x| + |-5| = |-45|

d) 6.x + x = 5¹¹ : 5⁹ + 3¹

e) 7.x - x = 5²¹ : 5¹⁵ + 3.2² - 7⁰

f ) 2^x : 2⁵ = 1

g) 2^x+1.2²⁰¹⁴ = 2²⁰¹⁵

h) | x - 5 | = 7 - (-3)

i) | - x - 16| = 31

k) &#x22EE;x;84&#x22EE;x;30&#x22EE;x" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-block; float:none; font-size:20.34px; font-style:normal; font-weight:normal; letter-spacing:normal; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; text-align:left; text-indent:0px; text-transform:none; white-space:nowrap; word-spacing:normal" class="MathJax_CHTML mjx-chtml">150⋮x;84⋮x;30⋮x$150⋮x;84⋮x;30⋮x$ và 0 < x < 16 ($x\in N$) &#x22EE;12;x&#x22EE;15;x&#x22EE;18" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-block; float:none; font-size:20.34px; font-style:normal; font-weight:normal; letter-spacing:normal; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; text-align:left; text-indent:0px; text-transform:none; white-space:nowrap; word-spacing:normal" class="MathJax_CHTML mjx-chtml">x⋮12;x⋮15;x⋮18$x⋮12;x⋮15;x⋮18$

l) &#x22EE;12;x&#x22EE;15;x&#x22EE;18" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-block; float:none; font-size:20.34px; font-style:normal; font-weight:normal; letter-spacing:normal; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; text-align:left; text-indent:0px; text-transform:none; white-space:nowrap; word-spacing:normal" class="MathJax_CHTML mjx-chtml">x⋮12;x⋮15;x⋮18$x⋮12;x⋮15;x⋮18$ và x < 150 ($x\in N$)

a) (x - 6)² = 9

b) 35 - 3.|x| = (2³ - 4)

c) |x| + |-5| = |-45|

d) 6.x + x = 5¹¹ : 5⁹ + 3¹

e) 7.x - x = 5²¹ : 5¹⁵ + 3.2² - 7⁰

f ) 2^x : 2⁵ = 1

g) 2^x+1.2²⁰¹⁴ = 2²⁰¹⁵

h) | x - 5 | = 7 - (-3)

i) | - x - 16| = 31

k) &#x22EE;x;84&#x22EE;x;30&#x22EE;x" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-block; float:none; font-size:20.34px; font-style:normal; font-weight:normal; letter-spacing:normal; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; text-align:left; text-indent:0px; text-transform:none; white-space:nowrap; word-spacing:normal" class="MathJax_CHTML mjx-chtml">150⋮x;84⋮x;30⋮x$150⋮x;84⋮x;30⋮x$ và 0 < x < 16 ($x\in N$) &#x22EE;12;x&#x22EE;15;x&#x22EE;18" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-block; float:none; font-size:20.34px; font-style:normal; font-weight:normal; letter-spacing:normal; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; text-align:left; text-indent:0px; text-transform:none; white-space:nowrap; word-spacing:normal" class="MathJax_CHTML mjx-chtml">x⋮12;x⋮15;x⋮18$x⋮12;x⋮15;x⋮18$

l) &#x22EE;12;x&#x22EE;15;x&#x22EE;18" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-block; float:none; font-size:20.34px; font-style:normal; font-weight:normal; letter-spacing:normal; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; text-align:left; text-indent:0px; text-transform:none; white-space:nowrap; word-spacing:normal" class="MathJax_CHTML mjx-chtml">x⋮12;x⋮15;x⋮18$x⋮12;x⋮15;x⋮18$ và x < 150 ($x\in N$)

tìm x ; y biết : 2.2" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:23.4px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">x2$x^2$.y + 3.x.y +2.x.2" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:23.4px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">y2$y^2$ + 3.2" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:23.4px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">y2$y^2$ = 10

1. tìm x ; y biết : ​ 3.x2" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:23.4px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">22" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:23.4px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">${\mathrm{<strong>x</strong>}}^{\mathrm{<strong>2</strong>}}$.y + 5. 2" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:23.4px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">x22" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:23.4px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">${\mathrm{<strong>x</strong>}}^{\mathrm{<strong>2</strong>}}$2" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:23.4px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml"> +2.x.2" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:23.4px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">+3y22" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:23.4px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">${\mathrm{<strong>y</strong>}}^{\mathrm{<strong>2</strong>}}$ + 5.2" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:23.4px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">y
   2" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:23.4px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">${\mathrm{<strong>y</strong>}}^{\mathrm{<strong>2</strong>}}$ = 16

Cho $P$=$\frac{1}{2}$ +$\frac{1}{3}$ +...+$\frac{1}{2019}$ và $Q$=$\frac{1}{2018}$ +$\frac{2}{2017}$ +$\frac{3}{2016}$ +...+$\frac{2016}{3}$ +$\frac{2017}{2}$ +$\frac{2018}{1}$ Tính (Q&#x2212;2019.P)2019" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:21.78px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal" class="MathJax_CHTML mjx-chtml">(Q−2019.P)2019$(Q-2019.P{)}^{2019}$