Question

If $(x^2+y^2=58)$ and $(x+y=10)$, then find the value of $(x^3+y^3)$.

Answer 1

Given,

$x^2+y^2=58$.....(1) and $x+y=10$......(2).

From (1) we get,

$x^2+y^2=58$

or, $(x+y{)}^2-2xy=58$

or, $100-58=2xy$

or, $44=2xy$

or, $xy=22$......(3).

Now $x^3+y^3=(x+y{)}^3-3xy(x+y)={10}^3-\mathrm{3.22.10}=340$. [ Using values of (2) and (3)]