If x^2 = 6 + √(6 + √(6 + √(6 + ....∞)), then what is one of the values

• Quant Quadratic

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

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

Answer

The given equation can be re-written as x² = 6 + √x²

x² = 6 + x

x² - x - 6 = 0

x² - 3x + 2x - 6 = 0

x(x - 3) + 2(x - 3) = 0

x = 3 or -2

The correct option is A.