Question

Number of real solution of $|x-3|=\sqrt{x-1}$ which are not prime

• A. $2$
• B. $3$
• C. $1$
• D. $0$

Answer 1

The correct option is D $0$

$|x-3|=\sqrt{x-1}$
$\because |x-3|\ge 0$
and
$\sqrt{x-1}\ge 0$
Since both the sides are always $\ge 0$
So, by squaring both the sides, we get
$\Rightarrow |x-3{|}^2=(\sqrt{x-1}{)}^2$
$\Rightarrow x^2+9-6x=x-1$
$\Rightarrow x^2-7x+10=0$
$\Rightarrow (x-5)(x-2)=0$
$\Rightarrow x=2,5$