How do you solve $x - 9 = sqrt(x - 3)$ ?

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Answer 1 · 2016-07-01T10:15:29

$x=12$

First you fix the domain of the solutions:

$x-3>=0 and x-9>=0$

that's $x>=9$

then you square both members:

$(x-9)^2=(sqrt(x-3))^2$

that's

$x^2-18x+81=x-3$

$x^2-18x+81-x+3=0$

$x^2-19x+84=0$

$x=(19+-sqrt(19^2-4*84))/2$

$x=(19+-5)/2$

$x=7 and x=12$

but only x=12 belongs to the calculated domain

How do you solve x - 9 = sqrt(x - 3)x - 9 = sqrt(x - 3)?