If $$ x+y=1 $$ , $$ x^2+y^2=3 $$ , find the value of $$ x^3+y^3 $$

Question

If $$ x+y=1 $$ , $$ x^2+y^2=3 $$ , find the value of  $$ x^3+y^3 $$

Uniteasy Admin · Accepted Answer

$$ x+y=1 \implies (x+y)^2 = 1$$
$$xy = \dfrac{ (x+y)^2 -x^2-y^2}{2} = \dfrac{1-3}{2} = -1 $$
$$x^3+y^3 $$
$$= (x+y)(x^2-xy+y^2) $$
$$= 2-(-1 )=3$$