If x + y + z = 2

xy + yz + zx = -11, then

Find x³ + y³ + z³ - 3xyz.

74

Here three variables and two eq. are given.

Put z = 0

x + y = 2

xy = -11

find, 

⇒ x³ + y³ + z³ - 3xyz = x³ + y³ + 0 - 0 = x³ + y³ 

⇒ (x + y)³ = x³ + y³ + 3xy (x + y)

⇒ 8 = x³ + y³ + 3 × -11 (2)

⇒ x³ + y³ = 74

Note → If the number of given variables are  more than the number of given equations then put all extra variables anything except \(\frac{1}{0}\) or \(\frac{0}{0}\) form.