An algebra problem by Hana Wehbi

Algebra Level 2

If x + 1 x = 2 x+\frac{1}{x}=2 then what is the value of x 2018 + 1 x 2018 = ? x^{2018}+\frac{1}{x^{2018}}=?


The answer is 2.

Hana Wehbi by Hana Wehbi , 51, USA

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1 solution

Hana Wehbi
Sep 29, 2018

If x + 1 x = 2 ⟹ x 2 + 1 = 2 x ⟹ ( x − 1 ) 2 = 0 ⟹ x = 1 \text{ If } x+\frac{1}{x}=2\implies x^2+1=2x \implies (x-1)^2=0\implies x=1 then the value of: x 2018 + 1 x 2018 = 1 + 1 = 2 x^{2018}+\frac{1}{x^{2018}}=1+1=2

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