Question

If $\sqrt{5x+9}$+$\sqrt{5x-9}$=$3(2-\sqrt2)$ then $\sqrt{10x+9}$ is equal to

• A. $3\sqrt7$
• B. $4\sqrt5$
• C. $3\sqrt31$
• D. $2\sqrt7$

Answer 1

Answer: (A)

$3\sqrt7$

Answer 2

Given:
$\sqrt{5x+9}+\sqrt{5x-9}=3(2+\sqrt2)$

$⇒$ $\sqrt{5x+9}+\sqrt{5x-9}=6+3\sqrt2$

$⇒$ $\sqrt{5x+9}+\sqrt{5x-9}=\sqrt{36}+\sqrt{18}$

By Comparing the LHS and RHS, we get:
$⇒$ $5x + 9 = 36$
$⇒$ $5x = 27$
$⇒$ $x =$ $\frac{27}{5}$ (can be verified using the second term as well).

$⇒$ $\sqrt{10x+9}$

= $\sqrt{(10\times\frac{27}{5})+9}$

= $\sqrt{63}=3\sqrt{7}$
So, the correct option is (A) : $3\sqrt7$.