Question

Number of solutions of the equation $\sqrt{3x-2}+\sqrt{4x+4}=\sqrt{5x+1}+\sqrt{4x-5}$ is

• A. $0$
• B. $1$
• C. $2$
• D. $4$

Answer 1

Answer: (B)

$1$

By Hit and Trial method we get to know that, $\sqrt{3x-2}+\sqrt{4x+4}=\sqrt{5x+1}+\sqrt{4x-5}$ holds true at $x=3$ only

as $\sqrt{3\ast 3-2}+\sqrt{4\ast 3+4}=\sqrt{5\ast 3+1}+\sqrt{4\ast 3-5}\Rightarrow \sqrt{7}+4=\sqrt{7}+4$

So, there is only one solution

Therefore, Answer is $1$