Question:
If \(\sqrt{5x+9}\)+\(\sqrt{5x-9}\)=\(3(2-\sqrt2)\) then \(\sqrt{10x+9}\) is equal to
If \(\sqrt{5x+9}\)+\(\sqrt{5x-9}\)=\(3(2-\sqrt2)\) then \(\sqrt{10x+9}\) is equal to
Updated On: Oct 1, 2024
- \(3\sqrt7\)
- \(4\sqrt5\)
- \(3\sqrt31\)
- \(2\sqrt7\)
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The Correct Option is A
Solution and Explanation
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) : \(3\sqrt7\).
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