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Algebra Level 2

Find a number whose sum with its inverse, is equal to 1

− 1 ± √ 5 i 2 \frac{-1±√5i}{2} 1 ± √ 3 i 2 \frac{1±√3i}{2} 1 ± √ 5 2 \frac{1±√5}{2} − 1 ± √ 3 2 \frac{-1±√3}{2}

Moaj Ahmed by Moaj Ahmed , 25, Bangladesh

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1 solution

Atomsky Jahid
Jul 16, 2019

Let the number be x x . Then, x + 1 x = 1 x + \frac{1}{x} = 1 Which leads to the quadratic equation x 2 − x + 1 = 0 x^2 - x +1 = 0 So, the solutions are x = 1 ± 3 i 2 x = \frac{1 \pm \sqrt{3} i}{2}

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