Question

giải pt:

a, (2x-5)² - (x+2)² =0

b, (3x² + 10x -8 )² =( 5x²-2x+10)²

 

 

Answer 1

a) \(\left(2x-5\right)^2-\left(x+2\right)^2=0\)

\(\Leftrightarrow\left(2x-5+x+2\right)\left(2x-5-x-2\right)=0\)

\(\Leftrightarrow\left(3x-3\right)\left(x-7\right)=0\)

b) Cách làm giống câu a

Answer 2

\(\left(3x^2+10x-8\right)^2=\left(5x^2-2x+10\right)^2\)

\(\Leftrightarrow\orbr{\begin{cases}3x^2+10x-8=5x^2-2x+10\\3x^2+10x-8=-5x^2+2x-10\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}2x^2-12x+18=0\\8x^2+8x+2=0\end{cases}}\)

\(TH1:2x^2-12x+18=0\)

\(\Leftrightarrow x^2-6x+9=0\)

\(\Leftrightarrow\left(x-3\right)^2=0\Leftrightarrow x=3\)

\(TH2:8x^2+8x+2=0\)

\(\Leftrightarrow4x^2+4x+1=0\)

\(\Leftrightarrow\left(2x+1\right)^2=0\)

\(\Leftrightarrow x=\frac{-1}{2}\)