An algebra problem by Arnab Kumar Debnath

Algebra Level 1

x + 1 x = 5 x + \frac{1}{x} = 5

x 2 + 1 x 2 = ? x^2 + \frac{1}{x^2} = ?


The answer is 23.

Arnab Kumar Debnath by Arnab Kumar Debnath , 21, Bangladesh

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1 solution

Alan Yan
Aug 10, 2015

( x + 1 x ) 2 = x 2 + 1 x 2 + 2 = 25 ⟹ x 2 + 1 x 2 = 23 (x+\frac{1}{x})^2 = x^2+\frac{1}{x^2}+2 = 25 \implies x^2 + \frac{1}{x^2} = \boxed{23}

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