SOLUTION: For what values of x is {{{ sqrt (9ax^2) = 3x (sqrt(a)) }}} a true statement? Assume a >= 0.

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Question 718135: For what values of x is +sqrt+%289ax%5E2%29+=+3x+%28sqrt%28a%29%29+ a true statement? Assume a >= 0.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
+sqrt+%289ax%5E2%29+=+3x+%28sqrt%28a%29%29+
The short solution is to simplify the square root on the left:
+sqrt+%289%29%2Asqrt%282%29%2Asqrt%28x%5E2%29+=+3x+%28sqrt%28a%29%29+
sqrt%289%29+=+3
but
sqrt%28x%5E2%29 is not x! It is abs%28x%29!
So the equation becomes:
3%2Asqrt%28a%29%2Aabs%28x%29+=+3x+%28sqrt%28a%29%29
Divide both sides by 3 and sqrt%28a%29 we get:
abs%28x%29+=+x
This says that x must be equal to its own absolute value. When is this true? It's true for any x that is not negative. So the x's that make
+sqrt+%289ax%5E2%29+=+3x+%28sqrt%28a%29%29+
a true statement are zero or any positive number.