Nice nested

Algebra Level 3

2 x 2 x 2 x 2 x . . . = x 2\sqrt{x\sqrt{2\sqrt{x\sqrt{2\sqrt{x\sqrt{2\sqrt{x...}}}}}}}=x

What is x x ?

16 16 32 32 4 2 4\sqrt{2} 2 2

Achraf Wassim by Achraf Wassim , 41, Egypt

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.

2 solutions

Unwrapping the coefficient and radical twice gives the equation x 2 16 = x ⇒ x 2 = 16 x ⇒ x = 16 \frac{x^2}{16}=x \Rightarrow x^2=16 x \Rightarrow x=16 .

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Simon Kaib
Jul 26, 2019

Assuming that the sum converges for some x ≠ 0 x\neq 0 : 2 x 2 x 2 x 2 x . . . = x 2\sqrt{x\sqrt{2\sqrt{x\sqrt{2\sqrt{x\sqrt{2\sqrt{x\sqrt{...}}}}}}}}=x we can make the following substitution: 2 x x = x 2\sqrt{x\sqrt{x}}=x , which yields x = 16 \boxed{x=16}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

same solution as me :D

Isaac YIU Math Studio - 1 year, 10 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...