.
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
- HOW TO evaluate expressions involving , , and
in this site.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lesson is the part of this online textbook under the topic "Evaluation, substitution".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.
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Again: This problem is to check your competency: whether you know the way . . .
It is very good for an interview . . . (on a mathematical position . . . )