SOLUTION: If m + n = 3 and m^2 + n^2 = 6, find the exact value of m^3 + n^3.

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Question 427410: If m + n = 3 and m^2 + n^2 = 6, find the exact value of m^3 + n^3.
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
The expression %28m+%2B+n%29%28m%5E2+%2B+n%5E2%29 is equal to .

Suppose we square both sides of m+%2B+n+=+3 to obtain m%5E2+%2B+2mn+%2B+n%5E2+=+9. Replacing m%5E2+%2B+n%5E2 we get 6+%2B+2mn+=+9 --> mn+=+3%2F2. Replace mn with 3%2F2 in our first equation to get

m%5E3+%2B+n%5E3+%2B+3%283%2F2%29+=+18 --> m%5E3+%2B+n%5E3+=+18+-+9%2F2+=+27%2F2.