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Algebra Level 1

Solve for x x :

x 2 − 2 = x x^{2} - 2 = x

-1 and 2 0 and 1 1 and -2 1 and 2

Heder Oliveira Dias by Heder Oliveira Dias , 38, Brazil

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3 solutions

Pushpesh Kumar
Jun 16, 2014

x 2 x^{2} - 2 = x

x 2 x^{2} - x - 2 = 0

x 2 x^{2} - 2x + x - 2 = 0

x ( x - 2 ) + 1 ( x - 2 ) = 0

( x - 2 ) ( x + 1) = 0

Case 1 : x - 2 = 0 , x = 2

Case 2 : x + 1 = 0 , x = -1

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Hassan Raza
Jul 31, 2014

G i v e n t h a t x 2 − 2 = x = > x 2 − x − 2 = 0 b y f a c t o r i z a t i o n = > x 2 − 2 x + x − 2 = 0 = > x ( x − 2 ) + 1 ( x − 2 ) = > ( x + 1 ) ( x − 2 ) = 0 E i t h e r x + 1 = 0 o r x − 2 = 0 x = − 1 o r x = 2 S . S = { − 1 , 2 } Given\quad that\\ \qquad { x }^{ 2 }-2=x\\ =>\quad { x }^{ 2 }-x-2=0\\ by\quad factorization\\ =>\quad { x }^{ 2 }-2x+x-2=0\\ =>\quad x(x-2)+1(x-2)\\ =>\quad (x+1)(x-2)=0\\ Either\\ x+1=0\quad or\quad x-2=0\\ x=-1\quad or\quad x=2\\ S.S=\boxed { \left\{ -1,2 \right\} }

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Prince Mishra
Jul 11, 2014

by factorization

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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