If x + y + z = 6, xyz = -10 and x2 + y2 + z2 = 30 , then what is the value of x3 + y3 + z3 = ?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 132.
( x + y + z)2 = x2 + y2 + z2 + 2(ab + bc + ac)
62 = 30 + 2(ab + bc + ac)
ab + bc + ac = 3
x3 + y3 + z3 - 3abc = (a + b + c)(a2 + b2 + c2 - ab - bc - ac)
x3 + y3 + z3 = 6(30 - 3) + 3(-10)
x3 + y3 + z3 = 162 - 30 = 132