Find value of √2+√2+√2+√2...
sorry, I have hard time to type the question. √2+ is inside square root another √2+, not answer 4√2.Hope you understand my question.
sorry, I have hard time to type the question. √2+ is inside square root another √2+, not answer 4√2.Hope you understand my question.
-
Let x = √2+√2+√2+√2..., then
x = sqrt(2 + (√2+√2+√2+√2...) )
= sqrt(2 + x)
x^2 - x - 2 = 0
(x-2)(x+1) = 0
x = 2, or -1. Since x must be > sqrt(2) > 0, the root -1 is dropped.
The answer is x = 2.
x = sqrt(2 + (√2+√2+√2+√2...) )
= sqrt(2 + x)
x^2 - x - 2 = 0
(x-2)(x+1) = 0
x = 2, or -1. Since x must be > sqrt(2) > 0, the root -1 is dropped.
The answer is x = 2.