Question

Tìm x, biết :

( 3x - 5 )^{2 -} (2x + 3 )² = 0

Answer 1

\(\left(3x-5\right)^2-\left(2x+3\right)^2=0\)
\(\Leftrightarrow9x^2-30x+25-4x^2-12x-9=0\)
\(\Leftrightarrow5x^2+18x+16=0\)
\(\Leftrightarrow5x^2+10x+8x+16=0\)
\(\Leftrightarrow5x\left(x+2\right)+8\left(x+2\right)=0\)
\(\Leftrightarrow\left(x+2\right)\left(5x+8\right)=0\)
\(\Leftrightarrow x+2=0\) hoặc \(5x+8=0\)
\(\odot x+2=0\Leftrightarrow x=-2\)
\(\odot5x+8=0\Leftrightarrow5x=-8\Leftrightarrow x=-\dfrac{8}{5}\)
Vậy \(S=\left\{-2;-\dfrac{8}{5}\right\}\)