SOLUTION: {{{x^2=21-sqrt(x^2-9)}}} Please help me get the solutions !! Thank you!!

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Question 438760: x%5E2=21-sqrt%28x%5E2-9%29
Please help me get the solutions !! Thank you!!
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2+-+9+=+12+-+sqrt%28x%5E2-9%29
<==> %28x%5E2+-+9%29+%2B+sqrt%28x%5E2+-+9%29+-+12+=+0
<==> %28sqrt%28x%5E2+-+9%29%29%5E2+%2B+sqrt%28x%5E2+-+9%29+-+12+=+0
<==> %28sqrt%28x%5E2+-+9%29+%2B+4%29%28sqrt%28x%5E2+-+9%29+-+3%29+=+0
==> sqrt%28x%5E2+-+9%29+-+3+=+0 ==> sqrt%28x%5E2+-+9%29+=+3
==> x%5E2+-+9+=+9 ==> x%5E2+=+18 ==> x+=+3sqrt%282%29, -3sqrt%282%29.
These two values satisfy the original equation, and so are the final answers.
(Note that we don't get real solutions from the equation sqrt%28x%5E2+-+9%29+%2B+4+=+0.