If x + y + z = 7, xy + yz + zx = 8, then what is the value of $x^3+y^3+z^3-3 x y z$ ?

175

If x + y + z = 7

xy + yz + zx = 8

 $x^3+y^3+z^3-3 x y z$ = ?

If the number of equation is less then the number of variables then we can put the extra variables according to our choice.

Here the number of variables are 3 and the number of equations are two than put z = 0

x + y = 7

xy = 8

x³+y³ = 7³ - 3 × 7  × 8 = 343 - 168 = 175