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Please solve this question step by step in notebook..

Answer»

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 = <klux>8</klux> * 7 = 8(8 - 1) \\ \\ \therefore y = 8


x + y = 3 + 8 = 11


11 is the answer.


Hope this may be helpful.


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Thank you. Have a nice DAY.



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