Question : If $\sqrt{5x-6}+\sqrt{5x+6}=6$, then what is the value of $x$?
Option 1: – 4
Option 2: 0
Option 3: 2
Option 4: 4
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Correct Answer: 2
Solution :
Given: $ \sqrt{5x-6}+\sqrt{5x+6}=6$
Squaring both sides,
⇒ $(\sqrt{5x-6}+\sqrt{5x+6})^2=6^2$
⇒ $(5x-6)+(5x+6)+2(\sqrt{5x-6}\sqrt{5x+6})=36$
⇒ $10x+2(\sqrt{25x^2-36} )=36$
⇒ $(\sqrt{25x^2-36} )=18-5x$
Again, squaring both sides,
⇒ $({25x^2-36} )=324+25x^2-180x$
⇒ $324+36 =180x$
⇒ $360 =180x$
⇒ $ x=\frac{360}{180}$
$\therefore x =2$
Hence, the correct answer is 2.
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