Complex linear system

Algebra Level 1

Solve for x x if x + 1 = t x +1 = t , x − 1 = s x - 1 = s , and t s = − 2 ts = -2 . Find x 2 x^2 .


The answer is -1.

Mattia Conti by Mattia Conti , 24, Italy

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2 solutions

Chew-Seong Cheong
Apr 10, 2018

{ x + 1 = t x − 1 = s ⟹ t s = ( x − 1 ) ( x + 1 ) = x 2 − 1 = − 2 ⟹ x 2 = − 1 \begin{cases} x+1 = t \\ x-1=s \end{cases} \implies ts = (x-1)(x+1) = x^2-1 = -2 \implies x^2 = \boxed{-1}

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Sir can u help me to understand a question. I have posted it in the form of note

A Former Brilliant Member - 3 years, 2 months ago
Mattia Conti
Apr 10, 2018

i + 1 = t i + 1 = t

i − 1 = s i - 1 = s

t ∗ s = ( i + 1 ) ( i − 1 ) = ( − 1 + i − i − 1 ) = − 2 t * s = (i + 1) (i - 1) = (-1 + i - i -1) = -2

so x = i = > x 2 = − 1 x = i => x^2 = -1

also x = -i solve the system, but ( − i ) 2 = − 1 (-i)^2 = -1

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