Question 1101935
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This is one example where giving the "obvious" answer without showing any work is of little help, because the solution by a formal algebraic process has some things that the student needs to watch our for.<br>
The given information says {{{x - sqrt(x) = 6}}}<br>
To solve, isolate the radical and square both sides:<br>
{{{x-6 = sqrt(x)}}}
{{{x^2-12x+36 = x}}}
{{{x^2-13x+36 = 0}}}
{{{(x-4)(x-9) = 0}}}<br>
The possible solutions are x=4 and x=9.<br>
But since, in solving the equation we squared both sides of the equation, we need to check for extraneous solutions.<br>
And indeed x=4 does not work: {{{4 - sqrt(4) = 4-2 = 2}}} is not equal to 6.<br>
But x=9 works: {{{9 - sqrt(9) = 9-3 = 6}}}.<br>
So the single solution is x=9.