Algebra manipulation: given $x+y = xy = 3$, evaluate $x^3 + y^3$

8.5k Views Asked by At

Tasked with a brainteaser, I am stuck on this one. The question follows:

Given $x+y = xy = 3$, evaluate $x^3 + y^3$

Can you solve this? If so, please provide the steps you took.

Attempt so far

1

There are 1 best solutions below

3
On

HINT: Expand $(x+y)^3$ and group the terms properly, and you’ll find that you can write it as a function of $x+y$ and $xy$. If you’re still stuck after giving that some thought, check the spoiler-protected block below.

$(x+y)^3=x^3+y^3+3xy(x+y)$