bai1
a,x(2-x)-2.x=x^2-5
(x-2).(x-1)+(x+1).x=6
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1x2= 2 1x2x3=6 1x2x3x4=24 1x2x3x4x5=120 1x2x3x4x5x6=720 1x2x3x4x5x6x7=5040
1x2x3x4x5x6x7x8=40320 1x2x3x4x5x6x7x8x9=362880 1x2x3x4x5x6x7x8x9x10=3628800
1 x 2 = 2
1 x 2 x 3 = 6
1 x 2 x 3 x 4 = 24
1 x 2 x 3 x 4 x 5 = 120
1 x 2 x 3 x 4 x 5 x 6 = 720
1 x 2 x 3 x 4 x 5 x 6 x 7 = 5040
1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 = 40320
1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 = 362880
1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 = 3628800
MẤY DÒNG NÀO BẠN THẤY KO CẦN THIẾT THÌ LƯỢC BỎ NHA!!!
a) \(2\left(x-5\right)-3\left(x+6\right)=4\left(x-7\right)\)
\(2x-10-3x-18=4x-28\)
\(2x-3x-4x-10-18=-28\)
\(-5x-28=-28\)
\(-5x=-28+28=0\)
\(x=\frac{0}{-5}=0\)
b) \(3\left(x-1\right)-2\left(x+5\right)=2\left(x-3\right)\)
\(3x-3-2x-10=2x-6\)
\(3x-2x-2x-3-10=-6\)
\(-x-13=-6\)
\(-x=-6+13=7\)
\(x=-7\)
c) \(5\left(1-x\right)-6\left(1+x\right)=7\left(3-x\right)\)
\(5-5x-6-6x=21-7x\)
\(-5x-6x+7x+5-6=21\)
\(-4x-1=21\)
\(-4x=22\)
\(x=\frac{22}{-4}=\frac{-11}{2}\)
d) \(2x+5-3\left(3x+7\right)=6\left(1-x\right)+8\)
\(2x+5-9x-21=6-6x+8\)
\(2x-9x+6x+5-21=6+8\)
\(-x-16=14\)
\(-x=14+16=30\)
\(x=-30\)
e) \(x-2+3\left(x-4\right)=5\left(x-6\right)+7\)
\(x-2+3x-12=5x-30+7\)
\(x+3x-5x-2-12=-30+7\)
\(-x-14=-23\)
\(-x=-23+14=-9\)
\(x=9\)
f) \(x+2+3\left(1-x\right)-5\left(2-x\right)=6\left(1-x\right)+\left(3-x\right)\)
\(x+2+3-3x-10+5x=6-6x+3-x\)
\(x-3x+5x+6x+x+2+3-10=6+3\)
\(10x-7=9\)
\(10x=9+7=16\)
\(x=\frac{16}{10}=\frac{8}{5}\)
1: \(\frac{3x-2}{3}-2=\frac{4x+1}{4}\)
=>\(\frac{3x-2-6}{3}=\frac{4x+1}{4}\)
=>\(\frac{3x-8}{3}=\frac{4x+1}{4}\)
=>3(4x+1)=4(3x-8)
=>12x+3=12x-32
=>3=-32(vô lý)
=>Phương trình vô nghiệm
2: \(\frac{x-3}{4}+\frac{2x-1}{3}=\frac{2-x}{6}\)
=>\(\frac{3\left(x-3\right)+4\left(2x-1\right)}{12}=\frac{2\left(2-x\right)}{12}\)
=>3(x-3)+4(2x-1)=2(2-x)
=>3x-9+8x-4=4-2x
=>11x-13=4-2x
=>13x=17
=>\(x=\frac{17}{13}\)
3: \(\frac12\left(x+1\right)+\frac14\left(x+3\right)=3-\frac13\left(x+2\right)\)
=>\(\frac12x+\frac12+\frac14x+\frac34+\frac13x+\frac23=3\)
=>\(x\left(\frac12+\frac14+\frac13\right)+\frac{6}{12}+\frac{9}{12}+\frac{8}{12}=3\)
=>\(x\left(\frac{6}{12}+\frac{3}{12}+\frac{4}{12}\right)=3-\frac{23}{12}=\frac{36}{12}-\frac{23}{12}=\frac{13}{12}\)
=>\(x\cdot\frac{13}{12}=\frac{13}{12}\)
=>x=1
4: \(\frac{x+4}{5}-x+4=\frac{x}{3}-\frac{x-2}{2}\)
=>\(\frac{x+4}{5}+\frac{5\left(-x+4\right)}{5}=\frac{2x-3\left(x-2\right)}{6}\)
=>\(\frac{x+4-5x+20}{5}=\frac{2x-3x+6}{6}\)
=>\(\frac{-4x+24}{5}=\frac{-x+6}{6}\)
=>6(-4x+24)=5(-x+6)
=>-24x+144=-5x+30
=>-19x=-114
=>x=6
5: \(\frac{4-5x}{6}=\frac{2\left(-x+1\right)}{2}\)
=>\(\frac{4-5x}{6}=-x+1\)
=>6(-x+1)=-5x+4
=>-6x+6=-5x+4
=>-6x+5x=4-6
=>-x=-2
=>x=2
6: \(-\left(\frac{x-3}{2}-2\right)=\frac{5\left(x+2\right)}{4}\)
=>\(-\frac{x-3-4}{2}=\frac{5\left(x+2\right)}{4}\)
=>\(\frac{-2\left(x-7\right)}{4}=\frac{5\left(x+2\right)}{4}\)
=>5(x+2)=-2(x-7)
=>5x+10=-2x+14
=>7x=4
=>x=4/7
7: \(\frac{2\left(2x+1\right)}{5}-\frac{6+x}{3}=\frac{5-4x}{15}\)
=>\(\frac{6\left(2x+1\right)-5\left(x+6\right)}{15}=\frac{5-4x}{15}\)
=>6(2x+1)-5(x+6)=-4x+5
=>12x+6-5x-30=-4x+5
=>7x-24=-4x+5
=>7x+4x=5+24
=>11x=29
=>\(x=\frac{29}{11}\)
8: \(\frac{7-3x}{2}-\frac{5+x}{5}=1\)
=>\(\frac{5\left(7-3x\right)-2\left(x+5\right)}{10}=1\)
=>5(7-3x)-2(x+5)=10
=>35-15x-2x-10=10
=>-17x+25=10
=>-17x=-15
=>x=15/17
1: (x+1)(y+2)=5
mà y+2>=2(do y là số tự nhiên)
nên (x+1;y+2)∈(1;5)
=>(x;y)∈(0;3)
2: (x+1)(y+2)=6
mà x+1>=1 và y+2>=2(do x,y là các số tự nhiên)
nên (x+1;y+2)∈{(3;2);(2;3);(1;6)}
=>(x;y)∈{(2;0);(1;1);(0;4)}
3: (x+2)(y+3)=6
mà x+2>=2 và y+3>=3(do x,y là các số tự nhiên)
nên (x+2;y+3)∈{(2;3)}
=>(x;y)∈(0;0)
4: (x-1)(y+3)=6
mà y+3>=3(do y là số tự nhiên)
nên (x-1;y+3)∈{(2;3);(1;6)}
=>(x;y)∈{(3;0);(2;3)}
5: (x-1)(y-3)=5
=>(x-1;y-3)∈{(1;5);(5;1)}
=>(x;y)∈{(4;8);(6;4)}
6: (x-2)(y-1)=3
=>(x-2;y-1)∈{(1;3);(3;1)}
=>(x;y)∈{(3;4);(5;2)}
7: (x-2)(y-1)=5
=>(x-2;y-1)∈{(1;5);(5;1)}
=>(x;y)∈{(3;6);(7;2)}
8: (x-3)(y+1)=7
mà y+1>=1(do y là số tự nhiên)
nên (x-3;y+1)∈{(1;7);(7;1)}
=>(x;y)∈{(4;6);(10;0)}
d: ĐKXĐ: \(x\notin\left\{2;-3\right\}\)
\(\dfrac{1}{x-2}-\dfrac{6}{x+3}=\dfrac{5}{6-x^2-x}\)
=>\(\dfrac{1}{x-2}-\dfrac{6}{x+3}=\dfrac{-5}{\left(x+3\right)\left(x-2\right)}\)
=>\(x+3-6\left(x-2\right)=-5\)
=>x+3-6x+12=-5
=>-5x+15=-5
=>-5x=-20
=>x=4(nhận)
e: ĐKXĐ: x<>-2
\(\dfrac{2}{x+2}-\dfrac{2x^2+16}{x^3+8}=\dfrac{5}{x^2-2x+4}\)
=>\(\dfrac{2}{x+2}-\dfrac{2x^2+16}{\left(x+2\right)\left(x^2-2x+4\right)}=\dfrac{5}{x^2-2x+4}\)
=>\(2\left(x^2-2x+4\right)-2x^2-16=5\left(x+2\right)\)
=>\(2x^2-4x+8-2x^2-16=5x+10\)
=>5x+10=-4x-8
=>9x=-18
=>x=-2(loại)
f: ĐKXĐ: \(x\in\left\{1;-1\right\}\)
\(\dfrac{x+1}{x^2+x+1}-\dfrac{x-1}{x^2-x+1}=\dfrac{2\left(x+2\right)^2}{x^6-1}\)
\(\Leftrightarrow\dfrac{x+1}{x^2+x+1}-\dfrac{x-1}{x^2-x+1}=\dfrac{2\left(x+2\right)^2}{\left(x-1\right)\left(x+1\right)\left(x^2+x+1\right)\left(x^2-x+1\right)}\)
=>\(\dfrac{\left(x+1\right)\left(x^2-x+1\right)\left(x^2-1\right)-\left(x-1\right)\left(x^2+x+1\right)\left(x^2-1\right)}{\left(x-1\right)\left(x+1\right)\left(x^2+x+1\right)\left(x^2-x+1\right)}=\dfrac{2\left(x+2\right)^2}{\left(x-1\right)\left(x+1\right)\left(x^2+x+1\right)\left(x^2-x+1\right)}\)
=>\(\left(x^3+1\right)\left(x^2-1\right)-\left(x^3-1\right)\left(x^2-1\right)=2\left(x^2+4x+4\right)\)
=>\(\left(x^2-1\right)\cdot\left(x^3+1-x^3+1\right)=2\left(x^2+4x+4\right)\)
=>\(2x^2+8x+8=\left(x^2-1\right)\cdot2=2x^2-2\)
=>8x=-10
=>x=-5/4(nhận)
huyển vế:
(x-2)(x-6)(x-3)(x-4)- 72X^2
(x-2)(x-6)
= (x^2 - ... +12)
số giữa:
-6x -2x = -8x
(x-3)(x-4)
= (x^2 ... +12)
số giữa:
-4x -3x = -7x
nhân 2 số giữa với nhau:
(-8x)(-7x) = +56x^2
-72x^2 +56x^2 = -16x^2 = (-16x)(x)
Đáp số:
(x^2 -16x +12)(x^2 +x +12)