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The largest value of $x$ that satisfies $\sqrt{x+1}=x$ can be written as $\dfrac{a+\sqrt{b}}{c}$ where $c$ has no common factor with $a$ and $\sqrt{b}$ and $b$ is not divisible by the square of any integer greater than 1. What is the value of $a+b+c$?

 Aug 14, 2020
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Squaring and solving the quadratic, we get x = (1 + sqrt(17))/8, so a + b + c = 1 + 17 + 8 = 26.

 Aug 14, 2020

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