If x^2 = 17x + y and y^2 = x + 17y, x \neq y, then what is the value of \sqrt{x^2+y^2+1}?

Explanation

Subtracting gives x^2 - y^2 = 16(x - y). Since x \neq y, x + y = 16. Adding gives x^2 + y^2 = 18(x + y) = 18 \times 16 = 288. Finally, \sqrt{x^2+y^2+1} = \sqrt{288+1} = 17.

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