Question : If $\sqrt{5 x - 6} + \sqrt{5 x + 6} = 6$ , then what is the value of $x$ ?
Option 1: – 4
Option 2: 0
Option 3: 2
Option 4: 4

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Question : If $x = \sqrt{- \sqrt{3} + \sqrt{3 + 8 \sqrt{7 + 4 \sqrt{3}}}}$ where $x > 0$ , then the value of $x$ is equal to:

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Answer 1

Correct Answer: 2

Solution : Given: $\sqrt{5 x - 6} + \sqrt{5 x + 6} = 6$
Squaring both sides,
⇒ $(\sqrt{5 x - 6} + \sqrt{5 x + 6})^{2} = 6^{2}$
⇒ $(5 x - 6) + (5 x + 6) + 2 (\sqrt{5 x - 6} \sqrt{5 x + 6}) = 36$
⇒ $10 x + 2 (\sqrt{25 x^{2} - 36}) = 36$
⇒ $(\sqrt{25 x^{2} - 36}) = 18 - 5 x$
Again, squaring both sides,
⇒ $(25 x^{2} - 36) = 324 + 25 x^{2} - 180 x$
⇒ $324 + 36 = 180 x$
⇒ $360 = 180 x$
⇒ $x = \frac{360}{180}$
$∴ x = 2$
Hence, the correct answer is 2.

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Question : If 5x−6+5x+6=6, then what is the value of x?Option 1: – 4Option 2: 0Option 3: 2Option 4: 4

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Question : If $\sqrt{5 x - 6} + \sqrt{5 x + 6} = 6$ , then what is the value of $x$ ?
Option 1: – 4
Option 2: 0
Option 3: 2
Option 4: 4