Question

Determine the value of x.
$\sqrt{5x^2-6x+8}-\sqrt{5x^2-6x-7}=1$

Answer 1

$\sqrt{5x^2-6x+8}-\sqrt{5x^2-6x-7}=1$

$\sqrt{5x^2-6x+8}=1+\sqrt{5x^2-6x-7}$

$5x^2-6x+8=1+5x^2-6x-7+2\sqrt{5x^2-6x-7}$

$2\sqrt{5x^2-6x-7}=14$

$\sqrt{5x^2-6x-7}=7$

$5x^2-6x-7-49=0$

$5x^2-20x+14x-56=0$

$(5x+14)(x-4)=0$

We get $x=4$ or $x=-\frac{14}{5}$