SOLUTION: If x and y are real, x^4y^5+x^5y^4 = 810 & x^6y^3+x^3y^6 = 945, Find 2x^3+(xy)^3+2y^3 = ?

Question 1020225: If x and y are real, x^4y^5+x^5y^4 = 810 & x^6y^3+x^3y^6 = 945, Find 2x^3+(xy)^3+2y^3 = ?
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
==> after factoring and changing the order of the terms.
==> (Equation A)
after multiplying both sides by 3.
Similarly, factor out from the 2nd equation :
(Equation B)
Add corresponding sides of Eqn. A and Eqn. B, to get

==>
==> xy(x+y) = 15, (Equation C)
after taking cube roots of both sides.
Now the first equation is the same as
(Equation D)
Dividing Eqn.D by Eqn.C, we get

Hence, (Equation E)
Putting into Eqn.B, we get
==> , or
(Equation F)
Finally, combining Equations E and F, we get
.

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