If x=

[Max@Math Revolution]

[GMAT math practice question]

If \(x=\sqrt{2+\sqrt{2+\sqrt{2+...}}}\) , \(y=\sqrt{3-\sqrt{3-\sqrt{3-...}}}\) and x^2 – x = a, y^2 + y = b. What is the value of a + b?

A. 1
B. 2
C. 3
D. 4
E. 5

[Max@Math Revolution]

=>

\(x=\sqrt{2+\sqrt{2+\sqrt{2+...}}}=\sqrt{2+x}\)
Then we have x^2 = 2 + x or x^2 – x = 2.
Thus a = 2.
\(y=\sqrt{3-\sqrt{3-\sqrt{3-...}}}=\sqrt{3-y}\)
Then we have y^2 = 3 - y or y^2 + y = 3.
Thus b = 3.

We have a + b = 2 + 3 = 5.

Therefore, E is the answer.
Answer: E