41st Problem

Algebra Level 3

If 6 + 4 2 = x + x \sqrt{6+4\sqrt2} = x+\sqrt x , find the value of x 6 x^6 .


The answer is 64.

Abhiram Rao by Abhiram Rao , 18, India

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2 solutions

6 + 4 2 = 2 ⋅ 3 + 2 2 = 2 ⋅ ( 1 + 2 ) 2 = 2 ⋅ ( 1 + 2 ) = 2 + 2 \sqrt{6+4\sqrt{2}} = \sqrt{2} \cdot \sqrt{3+2\sqrt{2}} = \sqrt{2} \cdot \sqrt{(1+\sqrt{2})^{2}} = \sqrt{2} \cdot (1+\sqrt{2}) = 2 + \sqrt{2}
x = 2 x = 2
x 6 = 64 x^{6} = 64

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Yeah. The same way.

Abhiram Rao - 5 years, 1 month ago
Sonia Gupta
Apr 25, 2016

Done in the same way

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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