If x + y + z = 3, and $x^2+y^2+z^2=101$, then what is the value of $\sqrt{x^3+y^3+z^3-3 x y z}$ ?

21

If x + y  = n

then, $x^3 + y^3$ = n³ - 3 × n × xy

( a + b )² = a² + b² + 2ab

If x + y + z = 3,

$x^2+y^2+z^2=101$

what is the value of  $\sqrt{x^3+y^3+z^3-3 x y z}$ ?

If the number of equations are less than the number of variables then we can put the extra variables according to our choice = 

So here two equations given and three variables are present so put z = 0

If x + y = 3,

$x^2+y^2=101$

( 3 )² = 101 + 2xy

xy = -46

The value of  $\sqrt{x^3+y^3}$ = \(\sqrt {3^3 - 3 × 3 × -46}\)

The value of  $\sqrt{x^3+y^3}$ = \(\sqrt {441}\) = 21