Question

please solve this question step by step in notebook..

Answer 1

Here, in the value of x, (√6 +) is repeating endlessly. So from right to left, as each square root is being passed through, the value always should be x.

∴ We can also write it as x = √(6 + x).

$x = \sqrt{6 + \sqrt{6 + \sqrt{6 + \sqrt{6 + ....}}}} = \sqrt{6 + x} \\ \\ x^2 = 6 + x \\ \\ x^2 - x = 6 \\ \\ = x(x - 1) = 6 = 3 * 2 = 3(3 - 1) \\ \\ \therefore x = 3$

The same is done in the case of y.

$y = \sqrt{56 + \sqrt{56 + \sqrt{56 + \sqrt{56 + ....}}}} = \sqrt{56 + y} \\ \\ y^2 = 56 + y \\ \\ y^2 - y = 56 \\ \\ = y(y - 1) = 56 = 8 * 7 = 8(8 - 1) \\ \\ \therefore y = 8$

x + y = 3 + 8 = 11

11 is the answer.

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