SOLUTION: If {{{a^2-2ab+b^2=36}}} and {{{a^2-3ab+b^2=22}}} find ab?

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Question 434499: If a%5E2-2ab%2Bb%5E2=36 and a%5E2-3ab%2Bb%5E2=22 find ab?
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
We have the system

a%5E2+-+2ab+%2B+b%5E2+=+36
a%5E2+-+3ab+%2B+b%5E2+=+22

If we multiply the second equation by -1,

a%5E2+-+2ab+%2B+b%5E2+=+36
-a%5E2+%2B+3ab+-+b%5E2+=+-22

Add the resulting two equations to obtain ab+=+14.