Roots of Roots

Algebra Level 2

4 + a + a + a + a + = 10 \large 4+\sqrt{a+\sqrt{a+\sqrt{a+\sqrt{a+\cdots}}}}= 10 What is the value of a a ?


The answer is 30.

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Akeel Howell
May 22, 2016

If 4 + a + a + a + a + = 10 4+\sqrt{a+\sqrt{a+\sqrt{a+\sqrt{a+\dotsb}}}}=10\\ Then a + a + a + a + = 10 4 = 6 \sqrt{a+\sqrt{a+\sqrt{a+\sqrt{a+\dotsb}}}}=10-4=6\\ a + a + a + a + a + = 36 \therefore a+\sqrt{a+\sqrt{a+\sqrt{a+\sqrt{a+\dotsb}}}}=36\\ So a + 6 = 36 a+6=36\\ a = 30 \therefore a=30\\

Great solution, Akeel. I upvoted your solution (+1)

Pranshu Gaba - 5 years ago

Log in to reply

Thank you.

Akeel Howell - 5 years ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...