SOLUTION: If x+y =3, then find x�+y�+10xy

Question 1126980: If x+y =3, then find x�+y�+10xy

Found 2 solutions by rothauserc, ikleyn:
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
Note that (a^3+b^3) = (a+b)(a^2−ab+b^2)
:
(x^3+y^3)+10xy = (x+y)(x^2-xy+y^2) +10xy =
:
3(x^2-xy+y^2) +10xy =
:
3x^2 -3xy +3y^2 +10xy =
:
3x^2 +7xy +3y^2
:

Answer by ikleyn(52864) (Show Source): You can put this solution on YOUR website!
.

= = in 3*xy*3 replace the second factor 3 by (x+y), based on what is given. Then you can continue this chain of equalities as = + = + xy = + xy = Replace (x+y) by 3 again, based on what is given. Then you can continue = + xy = 27 + xy. That is all that can be done.

Completed and solved.

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