If x + y + z = 10, x^2 + y^2 + z^2 = 30, then the value of x^3 + y^3…

If x + y  = n

then, $x^3 + y^3$ = n³ - 3 × n × xy

we also know that,

If $K+ l=n$

then, $K^2+l^2$ = n² – 2 × k × l

$x + y + z = 10, x^2 + y^2 + z^2 = 30$

Then the value of $x^3 + y^3 + z^3 - 3xyz$

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

$x + y = 10, x^2 + y^2 = 30$

 $x^2 + y^2$ = n² – 2 × x × y

30 = 10² – 2 × xy

xy = 35

Then the value of $x^3 + y^3$ = 10³ - 3 × 10 × 35

$x^3 + y^3$ = 1000 - 1050 = -50