Nested roots!

Algebra Level 4

$B$ is the number that evaluates the expression below. Find the largest two-digit value of $a$ such that

$\sqrt{a + \sqrt{a + \sqrt{a + \sqrt{a \ldots}}}}$

Evaluates to a positive integer.

Find $\dfrac ab$ .

1 solution

Justin Ruaya
Jan 17, 2016

Finally! I thought of $a=72$ first but I forgot $90$ .

Also, we can do it in this way

Obviously, $\sqrt{a+b}=b$ So $a+b=b^{2}$ We can get $a=b(b-1)$ .

A Former Brilliant Member - 5 years, 4 months ago