SOLUTION: If a+b=20 and ab=40, find a^2+b^2.

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Question 1077066: If a+b=20 and ab=40, find a^2+b^2.
Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.
a%5E2+%2B+b%5E2 = %28a%2Bb%29%5E2+-+2ab = 20%5E2+-+2%2A40 = 400 - 80 = 320.

SOLVED.

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It is the STANDARD way in which THIS problem MUST be solved.

Even do not try to find "a" and "b" explicitly and separately (although it is possible . . . ).
It would NOT be the way.


Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
%28a%2Bb%29%5E2=a%5E2%2B2ab%2Bb%5E2=a%5E2%2Bb%5E2%2B2%2Aab

Already given a+b=20, so the trinomial is 20%2A20=400


Also already given ab=40.
a%5E2%2Bb%5E2%2B2ab=400
a%5E2%2Bb%5E2%2B2%2A40=400
a%5E2%2Bb%5E2=400-2%2A40
a%5E2%2Bb%5E2=320