SOLUTION: how to solve x+y= 3 and xy= 1, then x²+y²= (?) and x^5 + y^5 = (?)

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Question 978041: how to solve x+y= 3 and xy= 1, then x²+y²= (?) and x^5 + y^5 = (?)
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Most important goal is solve for x and y.

x%283-x%29=1
-x%5E2%2B3x-1=0
x%5E2-3x%2B1=0

highlight%28x=%283-sqrt%285%29%29%2F2%29
and then
which is only one of the two x y pairs.


Evaluating the two requested expressions is a bunch of arithmetic.
(You might want to use Binomial Theorem.)