Infinite nested roots. Answer 2016 or maybe not? Try it.

Algebra Level 3

There is a function

$f\left( x \right) =\sqrt { x+\sqrt { x+\sqrt { x+\sqrt { x+.... } } } }$

and there are two numbers, $a$ and $b$ , both integers. It is known that:

1. $f(a) \times\ f(b) = 999$

2. $f(a) + f(b) = 64$

But, unfortunately a + b is uknown. Let change that!

The answer is 2034.

1 solution

Kay Xspre
Jan 7, 2016

We can write $f(x)$ as $(f(x))^2-f(x) = x$ . From $f(a)$ and $f(b)$ , we can conclude that $f(a) = 37$ and $f(b) = 27$ (swapping $a$ and $b$ would be unchanged). $a$ is then equal to $37^2-37 = 1332$ and $b$ equals to $27^2-27 = 702$ , thus, $a+b = 2034$

Infinite nested roots. Answer 2016 or maybe not? Try it.

The answer is 2034.

1 solution

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