Question

Number of rational roots of the equation $\sqrt{5x^2-6x+8}-\sqrt{5x^2-6x-7}=1$ is/are

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is B $2$

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

let $5x^2-6x=t$
$t+8=1+t-7+2\sqrt{t-7}$
$t-7=49$
$t=56$
$5x^2-6x=56.$
$\Rightarrow x=4,-\frac{14}{5}$
And both these values do not make the quantities under the roots in the original equation negative .
$\therefore$ Two rational roots .