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a) 2x2+3x-5=0
=> 2x2+5x-2x-5=0
=> x(2x+5)-(2x-5)=0
=> (2x-5)(x-1)=0
=> 2x-5=0, x-1=0
=> x=5/2; 1
\(2x^2+3x-5=0< =>2x^2-2+3x-3=0\)
\(< =>2\left(x+1\right)\left(x-1\right)-3\left(x-1\right)=0\)
\(< =>\left(x-1\right)\left(2x-1\right)=0< =>\orbr{\begin{cases}x=1\\x=\frac{1}{2}\end{cases}}\)
làm dùm bn 1 bài thôi
=( 2x -3 +x+5)(2x-3-x-5)=0
3x + 2=0
x = -2/3
x-8 =0
x = 8
x(2x-7)-4x+14=0
=> x(2x-7)-2(2x-7)=0
=> (x-2)(2x-7)=0
=> x=2 hoặc x=7/2
\(8x^3-27=0\)
\(\Leftrightarrow8x^3=27\)
\(\Leftrightarrow x^3=\frac{27}{8}\)
\(\Leftrightarrow x=\frac{3}{2}\)
\(2x^3+x^2-8x-4=0\)
\(\Leftrightarrow\)\(x^2\left(2x+1\right)-4\left(2x+1\right)=0\)
\(\Leftrightarrow\)\(\left(2x+1\right)\left(x^2-4\right)=0\)
\(\Leftrightarrow\)\(\left(2x+1\right)\left(x-2\right)\left(x+2\right)=0\)
đến đây bạn làm tiếp nha
\(2x^3+x^2-8x-4=0\)
\(x^2\left(2x+1\right)-4\left(2x+1\right)=0\)
\(\left(x^2-4\right)\left(2x+1\right)=0\)
\(1.x^2-4=0\)
\(\left(x-2\right)\left(x+2\right)=0\)
\(\Rightarrow x=\pm2\)
\(2.2x+1=0\)
\(x=-\frac{1}{2}\)
a) \(x^3+3x^2+3x+2=0\)
<=> \(x^3+x^2+x+2x^2+2x+2=0\)
<=> \(x\left(x^2+x+1\right)+2\left(x^2+x+1\right)=0\)
<=> \(\left(x+2\right)\left(x^2+x+1\right)=0\)
tự làm
b) \(x^4-2x^3+2x-1=0\)
<=> \(\left(x^4-3x^3+3x^2-x\right)+\left(x^3-3x^2+3x-1\right)=0\)
<=> \(x\left(x^3-3x^2+3x-1\right)+\left(x^3-3x^2+3x-1\right)=0\)
<=> \(\left(x^3-3x^2+3x-1\right)\left(x+1\right)=0\)
<=> \(\left(x-1\right)^3\left(x+1\right)=0\)
tự làm
c) \(x^4-3x^3-6x^2+8x=0\)
<=> \(x\left(x^3-3x^2-6x+8\right)=0\)
<=> \(x\left[\left(x^3+x^2-2x\right)-\left(4x^2+4x-8\right)\right]=0\)
<=>\(x\left[x\left(x^2+x-2\right)-4\left(x^2+x-2\right)\right]=0\)
<=> \(x\left(x-4\right)\left(x^2+x-2\right)=0\)
<=> \(x\left(x-4\right)\left(x-1\right)\left(x+2\right)=0\)
tự làm
\(x^2\left(2x-3\right)-12+8x=0\)
\(\Leftrightarrow x^2\left(2x-3\right)+\left(8x-12\right)=0\)
\(\Leftrightarrow x^2\left(2x-3\right)+4\left(2x-3\right)=0\)
\(\Leftrightarrow\left(x^2+4\right)\left(2x-3\right)=0\)
\(\Leftrightarrow x^2+4=0\)hoặc \(2x-3=0\)
\(TH:x^2+4=0\Rightarrow x^2=-4\)( vô nghiệm )
\(TH:2x-3=0\Rightarrow x=\frac{3}{2}\)( thỏa mãn )
Vậy \(x=\frac{3}{2}\)
\(8x^3-2x=0\)
\(\Rightarrow2x\left(4x^2-1\right)=0\)
\(\Rightarrow2x\left(2x-1\right)\left(2x+1\right)=0\)
Trường hợp 1: \(2x=0\Rightarrow x=0\)
Trường hợp 2: \(2x-1=0\Rightarrow2x=1\Rightarrow x=\frac{1}{2}\)
Trường hợp 3: \(2x+1=0\Rightarrow2x=-1\Rightarrow x=\frac{-1}{2}\)