Question

What is a possible value of $x$, if $\sqrt{2x+3}-1=x$?

• A. $\sqrt{2}$
• B. $\sqrt{3}$
• C. $\sqrt{5}$
• D. $\sqrt{7}$
• E. $\sqrt{11}$

Answer 1

Answer: (A)

$\sqrt{2}$

Given, $\sqrt{2x+3}-1=x$
$\Rightarrow \sqrt{2x+3}=x+1$

$\Rightarrow {\left(\sqrt{2x+3}\right)}^2={(x+1)}^2$(On squaring both sides)

$\Rightarrow 2x+3=x^2+2x+1$
$\Rightarrow x^2=2$
$x=\sqrt{2}$