If x + y + z = 3, and $x^2+y^2+z^2=101$, then what is the value of $\sqrt{x^3+y^3+z^3-3 x y z}$ ?
Answer & explanation
Correct answer: option 2
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