Let me show you the RIGHT WAY solving this problem.
We are given
x + y = 1.
Cube both sides. You will get
1 = = + .
Now replace by 19 ( ! given !) and replace (x+y) by 1 in the right side. You will get
1 = 19 + 3xy, which implies 3xy = 1 - 19 = -18.
Hence, xy = = -6.
Now the last step is
= = 1 - 2xy = 1 - 2*(-6) = 1 + 12 = 13.
Answer. x^2 + y^2 = 13.
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It is how this problem MUST be solved, and it is how IT IS EXPECTED you will solve it (if you know the way !)
Any other way is the way to N O W H E R E.
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If you want to see other similar solved problems, look into the lesson
