If x 2 = 6 + √ 6 + √6 + √6 + .... ∞ , then what is one of the value of x equal to?

Q: If x 2 = 6 + √ 6 + √6 + √6 + .... ∞ , then what is one of the value of x equal to?

Here, x2 = 6 + √6 + √6 + √6 + .... ∞ , So, x2 = 6 + √x2 ⇒ x2 = 6 + x ⇒ x2 - x - 6 = 0 ⇒ x2 + 2x - 3x - 6 = 0 ⇒ x(x + 2) - 3(x + 2) = 0 ⇒ (x - 3) (x + 2) = 0 ∴ x = 3

6
5
4
3

Correct Answer: 3

Explanation:

Here, x² = 6 + √6 + √6 + √6 + .... ∞ ,
So, x² = 6 + √x²
⇒ x² = 6 + x
⇒ x² - x - 6 = 0
⇒ x² + 2x - 3x - 6 = 0
⇒ x(x + 2) - 3(x + 2) = 0
⇒ (x - 3) (x + 2) = 0
∴ x = 3

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