Question

Solution of the equation $\sqrt{x+10}+\sqrt{x-2}=6$ are

• A. $0$
• B. $6$
• C. $4$
• D. none of these

Answer 1

The correct option is B

$6$

Explanation for the correct answer:

Solving the given equation for $x$:

We have the equation as: $\sqrt{x+10}+\sqrt{x-2}=6$

Squaring on both the sides, we get:

$$\begin{gathered} \Rightarrow {\left(\sqrt{x+10}\right)}^2+{\left(\sqrt{x–2}\right)}^2+2\left(\sqrt{x+10}\right)\left(\sqrt{x–2}\right)=36 \\ \Rightarrow x+10+x-2+2\left(\sqrt{x+10}\right)\left(\sqrt{x–2}\right)=36 \\ \Rightarrow 2x+8–36=-2\left(\sqrt{x+10}\right)\left(\sqrt{x–2}\right) \\ \Rightarrow 2x–28=-2\left(\sqrt{x+10}\right)\left(\sqrt{x–2}\right) \\ \Rightarrow x-14=-\left(\sqrt{x+10}\right)\left(\sqrt{x–2}\right) \end{gathered}$$

Squaring on both the sides, again

$$\begin{gathered} \Rightarrow {(x-14)}^2=-\left(\sqrt{x+10}\right){\left(\sqrt{x–2}\right)}^2 \\ \Rightarrow x^2–28x+196=(x+10)(x–2) \\ \Rightarrow x^2–28x+196=(x^2+8x–20) \\ \Rightarrow -36x=-216 \\ \Rightarrow x=6 \end{gathered}$$

Therefore, the correct answer is option (B).