Question

Tìm `x`

$\sqrt{2x + 5}$ - $\sqrt{3x - 5}$ = `2`

 

Answer 1

ĐKXĐ: \(x\ge\dfrac{5}{3}\)

\(pt\Leftrightarrow2x+5+3x-5-2\sqrt{\left(2x+5\right)\left(3x-5\right)}=4\)

\(\Leftrightarrow5x-4=2\sqrt{\left(2x+5\right)\left(3x-5\right)}\)

\(\Leftrightarrow25x^2-40x+16=4\left(6x^2+5x-25\right)\)

\(\Leftrightarrow x^2-60x+116=0\)

\(\Leftrightarrow\left(x-58\right)\left(x-2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=58\left(tm\right)\\x=2\left(tm\right)\end{matrix}\right.\)