Question

If $\sqrt{x}+\sqrt{y}=\sqrt{18+6\sqrt{5}},$ find the value of $x$.

• A. $12$
• B. $15$
• C. $6$
• D. $8$

Answer 1

Answer: (B)

$15$

The given expression is $\sqrt{x}+\sqrt{y}=\sqrt{18+6\sqrt{5}}$

After squaring both side terms we get, $x+y+2\sqrt{xy}=18+6\sqrt{5}$

By comparing both side terms we can assume, $x+y=18$ and $2\sqrt{xy}=6\sqrt{5}$ Or $xy=45$

$\Rightarrow x+y=18$ ....$\left(1\right)$

$\Rightarrow xy=45$ ......$\left(2\right)$

From equation $\left(1\right)$ and $\left(2\right)$ we can say that $x=15,y=3$ or $x=3,y=15$

Hence the value of $x$ can be either $15$ or $3$.

Hence, the answer is $15$.