SOLUTION: If {{{x+y=2}}} and {{{ x*y=23}}} what is {{{x^2+y^2}}}?

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Question 1083617: If x%2By=2 and +x%2Ay=23 what is x%5E2%2By%5E2?
Answer by ikleyn(52856) About Me  (Show Source):
You can put this solution on YOUR website!
.
If x + y = 2 then (squaring both sides)

x%5E2+%2B+2xy+%2B+y%5E2 = 4.


Subtract 2xy from the left side and subtract the equal value 2*23 = 46 from the right side, and you will get the 


ANSWER: x%5E2+%2B+y%5E2 = 4 - 46 = -42.

Surely, the pair (x,y) is not a pair of real numbers.

They are COMPLEX numbers, instead.