If x2 = 6 + √6 + √6 + √6 + .... ∞

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If x² = 6 + √6 + √6 + √6 + .... ∞ , then what is one of the value of x equal to ?

1. 6
2. 5
3. 4
4. 3

Correct Option: D

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