SOLUTION: solve for x {{{sqrt(x-2)=x-4}}}

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Question 1055411: solve for x
sqrt%28x-2%29=x-4

Answer by ikleyn(52884) About Me  (Show Source):
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solve for x
sqrt%28x-2%29=x-4
~~~~~~~~~~~~~~~~~~~~~~~

sqrt%28x-2%29 = x-4.

Square both sides

x - 2 = x%5E2+-+8x+%2B+16.

x%5E2+-9x+%2B18 = 0.

Factor left side

(x-3)*(x-6) = 0.

The roots are x= 3  and  x= 6.

Only x = 6 satisfies the original equation.

Answer. The solution is x= 6.