An algebra problem by Bruno Mack

Algebra Level 2

Given: x 2 = 1 3 y x^{2} = \frac{1}{3y} 2 x = y 2 2x = y^{2}

Find the only real solution for x.


The answer is 0.56097757272309974292.

Bruno Mack by Bruno Mack , 37, USA

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1 solution

Paola Ramírez
Jul 16, 2015

( x 2 ) 2 = ( 1 3 y ) 2 (x^2)^2=(\frac{1}{3y})^2

x 4 = 1 9 y 2 x^4=\frac{1}{9y^2}

⇒ \Rightarrow x 4 = 1 9 ( 2 x ) = 1 18 x ) ⇒ x 5 = 1 18 ∴ x = 1 18 5 ≈ 0.561 x^4=\frac{1}{9(2x)}=\frac{1}{18x)}\Rightarrow x^5=\frac{1}{18}\therefore x=\sqrt[5]{\frac{1}{18}}\approx 0.561

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