Question

Solve the following equations:
$\sqrt{2x^2+5x-2}-\sqrt{2x^2+5x-9}=1$.

Answer 1

$\sqrt{2x^2+5x-2}-\sqrt{2x^2+5x-9}=1$

Put $2x^2+5x=t$

$\sqrt{t-2}-\sqrt{t-9}=1\sqrt{t-2}=1+\sqrt{t-9}$

squaring both sides

$2\sqrt{t-9}=6\sqrt{t-9}=3$

Again squaring both sides

$t-9=9t=182x^2+5x=t2x^2+5x=182x^2+5x-18=02x^2-4x+9x-18=02x(x-2)+9(x-2)=0(2x+9)(x-2)=0x=-\frac{9}{2},2$