SOLUTION: Solve the equation and check for extraneous solutions. square root 9a^2 +a-7 = 3a

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Question 80571: Solve the equation and check for extraneous solutions.
square root 9a^2 +a-7 = 3a
Answer by mathdoc314(58) About Me  (Show Source):
You can put this solution on YOUR website!
I guess that means you want values of a for which
+sqrt%289%2Aa%5E2+%2B+a+-+7%29+=+3a+
The extraneous solutions that can occur are ones with +a+%3C+0+
since the left side is always nonnegative. (The question doesn't ask for solutions where + or - square root of 9a^2 + a - 7 is 3a.)
Square both sides
+9%2Aa%5E2+%2B+a+-+7+=+9%2Aa%5E2+ and +a%3E=0+
Subtract 9*a^2 from both sides
+a-7+=+0+ and +a%3E=+0+
+a+=+7+
Check your answer:
+sqrt%289%2A7%5E2+%2B+7+-+7%29+=+3%2A7+ ?
+sqrt%28441%29+=+21+ TRUE