A Challenge

Algebra Level 1

Can you solve this?


The answer is 5.

Melanie Lynx by Melanie Lynx , 27, Indonesia

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3 solutions

Julian Poon
Sep 5, 2014

The equation can be written as:

5 x = x \sqrt { 5x } =x

Solving for it gives

x = 5 x=5\quad or 0 \quad 0

Since x > 5 x>\sqrt { 5 } , x = 5 x=5

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Kartik Kulkarni
Jan 6, 2015

Let the answer be x x

x = 5 5 5 ⋅ ⋅ ⋅ x = \sqrt{5 \sqrt {5 \sqrt{5 \sqrt {\cdot \cdot \cdot}}}}

x = 5 ( 5 5 ⋅ ⋅ ⋅ ) x = \sqrt{5( \sqrt {5 \sqrt{5 \sqrt {\cdot \cdot \cdot})}}}

Therefore x = 5 ( x ) x = \sqrt{5(x)}

x 2 = 5 x x^{2} = 5x

And x = 5 x = \boxed{5}

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Archiet Dev
Oct 2, 2014

Why this question is so much popular?I have seen this exact question(same no.s) on brilliant about 15 times...!

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Thats because it can have so many different variations, ranging from level 1 to level 5. Its so interesting.

Julian Poon - 6 years, 6 months ago

I've only seen this problem once.

A Former Brilliant Member - 3 years, 1 month ago

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