Bài 2: Tính giá trị của các biểu thức sau bằng cách tính nhanh nhất:
a) 21/25 .11/9.5/7 b) 5/23.17/26+5/23.9/26 c)7/13.5/19+7/19.8/13- ba , bảy phần 19
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Bài 2 :
a, \(A=\left|2x-4\right|+2\ge2\)
Dấu ''='' xảy ra khi x = 2
Vậy GTNN A là 2 khi x = 2
b, \(B=\left|x+2\right|-3\ge-3\)
Dấu ''='' xảy ra khi x = -2
Vậy GTNN B là -3 khi x = -2
voi x =1
=>M= (1-5)2 +2017
M= (-4)2 +2017
M= 16 + 2017
M=2033
Vậy M = 2033
b) gia tri nho nhat cua bieu thuc là 2017
a: \(A=0x^2y^4z+\dfrac{7}{2}x^2y^4z-\dfrac{2}{5}x^2y^4z=\dfrac{31}{10}x^2y^4z=\dfrac{31}{10}\cdot2^2\cdot\dfrac{1}{16}\cdot\left(-1\right)=-\dfrac{31}{40}\)
a: \(=\dfrac{7}{5}x^4z^3y=\dfrac{7}{5}\cdot2^4\cdot\left(-1\right)^3\cdot\dfrac{1}{2}=-\dfrac{56}{5}\)
b: \(=-xy^3\)
a, \(A=-x^2-2x+3=-\left(x^2+2x-3\right)=-\left(x^2+2x+1-4\right)\)
\(=-\left(x+1\right)^2+4\le4\)
Dấu ''='' xảy ra khi x = -1
Vậy GTLN là 4 khi x = -1
b, \(B=-4x^2+4x-3=-\left(4x^2-4x+3\right)=-\left(4x^2-4x+1+2\right)\)
\(=-\left(2x-1\right)^2-2\le-2\)
Dấu ''='' xảy ra khi x = 1/2
Vậy GTLN B là -2 khi x = 1/2
c, \(C=-x^2+6x-15=-\left(x^2-2x+15\right)=-\left(x^2-2x+1+14\right)\)
\(=-\left(x-1\right)^2-14\le-14\)
Vâỵ GTLN C là -14 khi x = 1
Bài 8 :
b, \(B=x^2-6x+11=x^2-6x+9+2=\left(x-3\right)^2+2\ge2\)
Dấu ''='' xảy ra khi x = 3
Vậy GTNN B là 2 khi x = 3
c, \(x^2-x+1=x^2-x+\dfrac{1}{4}+\dfrac{3}{4}=\left(x-\dfrac{1}{2}\right)^2+\dfrac{3}{4}\ge\dfrac{3}{4}\)
Dấu ''='' xảy ra khi x = 1/2
Vậy ...
c, \(x^2-12x+2=x^2-12x+36-34=\left(x-6\right)^2-34\ge-34\)
Dấu ''='' xảy ra khi x = 6
Vậy ...
\(\text{A= 73 - (35 + 1𝑎) : 23}\)
thay \(a=45\) vào biểu thức ta có:
\(A=73-\left(35+45\right):23\)
\(=73-\frac{80}{23}=\frac{1599}{23}\)
b)\(73-\left(35+1a\right):23=1715\)
\(\left(35+1a\right):23=-1642\)
\(35+a=-37766\)
\(a=-37801\)
Bài 3:
a: \(M=4x^2-20x+25\)
\(=\left(2x\right)^2-2\cdot2x\cdot5+5^2\)
\(=\left(2x-5\right)^2=\left(2\cdot\frac{105}{2}-5\right)^2=\left(105-5\right)^2=100^2=10000\)
b: \(x^3-\frac19x=0\)
=>\(x\left(x^2-\frac19\right)=0\)
=>\(x\left(x-\frac13\right)\left(x+\frac13\right)=0\)
=>\(\left[\begin{array}{l}x=0\\ x-\frac13=0\\ x+\frac13=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=0\\ x=\frac13\\ x=-\frac13\end{array}\right.\)
Bài 2:
a: \(6x^3y-9x^2y^2=3x^2y\cdot2x-3x^2y\cdot3y\)
\(=3x^2y\left(2x-3y\right)\)
b: \(4x^2-25=\left(2x\right)^2-5^2=\left(2x-5\right)\left(2x+5\right)\)
Bài 4:
\(A=2x^2-15\ge-15\\ A_{min}=-15\Leftrightarrow x=0\\ B=2\left(x+1\right)^2-17\ge-17\\ B_{min}=-17\Leftrightarrow x=-1\)
Bài 5:
\(A=-x^2+14\le14\\ A_{max}=14\Leftrightarrow x=0\\ B=25-\left(x-2\right)^2\le25\\ B_{max}=25\Leftrightarrow x=2\)
ĐKXĐ : \(x\ne0;x\ne\pm1\)
a) Bạn ghi lại rõ đề.
b) \(B=\dfrac{x-1}{x+1}+\dfrac{3x-x^2}{x^2-1}=\dfrac{x-1}{x+1}+\dfrac{3x-x^2}{\left(x-1\right).\left(x+1\right)}\)
\(=\dfrac{\left(x-1\right)^2+3x-x^2}{\left(x-1\right).\left(x+1\right)}=\dfrac{x+1}{\left(x-1\right).\left(x+1\right)}=\dfrac{1}{x-1}\)
c) \(P=A.B=\dfrac{x^2+x-2}{x.\left(x-1\right)}=\dfrac{\left(x-1\right).\left(x+2\right)}{x\left(x-1\right)}=\dfrac{x+2}{x}=1+\dfrac{2}{x}\)
Không tồn tại Min P \(\forall x\inℝ\)
a: \(\dfrac{21}{25}\cdot\dfrac{11}{9}\cdot\dfrac{5}{7}=\dfrac{21}{7}\cdot\dfrac{5}{25}\cdot\dfrac{11}{9}\)
\(=3\cdot\dfrac{11}{9}\cdot\dfrac{1}{5}=\dfrac{11}{3}\cdot\dfrac{1}{5}=\dfrac{11}{15}\)
b: \(\dfrac{5}{23}\cdot\dfrac{17}{26}+\dfrac{5}{23}\cdot\dfrac{9}{26}\)
\(=\dfrac{5}{23}\left(\dfrac{17}{26}+\dfrac{9}{26}\right)\)
\(=\dfrac{5}{23}\cdot1=\dfrac{5}{23}\)
c: \(\dfrac{7}{13}\cdot\dfrac{5}{19}+\dfrac{7}{19}\cdot\dfrac{8}{13}-3\dfrac{7}{19}\)
\(=\dfrac{7}{19}\left(\dfrac{5}{13}+\dfrac{8}{13}\right)-3-\dfrac{7}{19}\)
\(=\dfrac{7}{19}-3-\dfrac{7}{19}=-3\)
\(a,\dfrac{21}{25}.\dfrac{11}{9}.\dfrac{5}{7}\)
\(=\dfrac{21.11.5}{25.9.7}\)
\(=\dfrac{1.11.1}{5.3.1}\)
\(=\dfrac{11}{15}\)
\(b,\dfrac{5}{23}.\dfrac{17}{26}+\dfrac{5}{23}.\dfrac{9}{26}\)
\(=\dfrac{5}{23}.\left(\dfrac{17}{26}+\dfrac{9}{26}\right)\)
\(=\dfrac{5}{23}.1\)
\(=\dfrac{5}{23}\)
\(c,\dfrac{7}{13}.\dfrac{5}{19}+\dfrac{7}{19}.\dfrac{8}{13}\)
\(=\dfrac{7}{19}.\dfrac{5}{13}+\dfrac{7}{19}.\dfrac{8}{13}\)
\(=\dfrac{7}{19}.\left(\dfrac{5}{13}+\dfrac{8}{13}\right)\)
\(=\dfrac{7}{19}.1\)
\(=\dfrac{7}{19}\)