Question

Solve $\sqrt{25-x^2}=x-1$

• A. $x=-4,3$
• B. $x=4,-3$
• C. $x-4,3$
• D. $x=-4,-3$

Answer 1

The correct option is B $x=4,-3$

Given, $\sqrt{25-x^2}=x-1$

Squaring both sides, we have

${\left(\sqrt{25-x^2}\right)}^2={(x-1)}^2$

$\Rightarrow 25-x^2=x^2+1-2x$ .......... $a^2-b^2=(a-b)(a+b)$

$\Rightarrow 2x^2-2x-24=0$

$\Rightarrow (x-4)(2x+6)=0$

$\Rightarrow x=4\text{or}-3$

Solution:- (B) $x=4,-3$