Problem No. 51

Algebra Level 3


The answer is 10.

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1 solution

Hobart Pao
Aug 19, 2015

There's probably an easier way to solve? This is a standard approach. ( x + 3 x + 6 + x 3 x + 6 = 6 ) 2 \left(\sqrt{x+\sqrt{3x+6}} + \sqrt{x-\sqrt{3x+6}} = 6\right)^{2} 2 x + 2 x 2 ( 3 x + 6 ) = 36 2x+2\sqrt{x^{2}-(3x+6)}= 36 x + x 2 3 x 6 = 18 x+\sqrt{x^{2}-3x-6}=18 x 2 3 x 6 = 18 x \sqrt{x^{2}-3x-6}=18-x x 2 3 x 6 = x 2 36 x + 324 x^{2} - 3x - 6 = x^{2}-36x+324 330 = 33 x 330=33x x = 10 x=\boxed{10}

Good solution

Rama Devi - 5 years, 9 months ago

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