How do you solve sqrt(x-2)=x-2?

2 Answers
Monzur R.
Jul 19, 2017

x = 2 or x=3

Explanation:

sqrt(x-2) = x-2

If we let alpha = x-2, then sqrtalpha = alpha. We know that this can only be the case if alpha = 0 or alpha =1. Then x = 0+2 or x=1+2.

Narad T.
Jul 19, 2017

The solutions are S={2,3}

Explanation:

Squaring the LHS and the RHS

sqrt(x-2)=x-2

(sqrt(x-2))^2=(x-2)^2

x^2-4x+4=color(red)(x-2)

x^2-4xcolor(red)(-x)+4color(red)(+2)=0

x^2-5x+6=0

Factorising

(x-2)(x-3)=0

Therefore,

(x-2)=0, =>, x=2

(x-3)=0, =>, x=3

Verification

sqrt(2-2)=2-2

sqrt(3-2)=3-2

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