The Easy Equality

Algebra Level 2

If x 2 + 1 x 2 = 102 x^2 + \dfrac1{x^2} = 102 , find ∣ x − 1 x ∣ \left | x - \dfrac1x \right| .


The answer is 10.

Jason Chrysoprase by Jason Chrysoprase , 18, Indonesia

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1 solution

Jason Chrysoprase
Jan 28, 2016

( x − 1 x ) 2 ( x - \frac{1}{x})^2 = x 2 + 1 x 2 − 2 x^2 + \frac{1}{x^2} -2

( x − 1 x ) 2 ( x - \frac{1}{x})^2 = 102 − 2 102 -2

( x − 1 x ) 2 ( x - \frac{1}{x})^2 = 100 100

x − 1 x x - \frac{1}{x} = 10 10

Get ready for the medium !!!

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