If x + y + z = 3, x2 + y2 + z2 = 45 and x3 + y3 + z3 = 69, then what is the value of xyz ?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. - 40.
We have given that in the question
x + y + z = 3, x2 + y2 + z2 = 45 and x3 + y3 + z3 = 69
(x + y + z)2 = x2 + y2 + z2 + 2(xy + yz + zx)
9 = 45 + 2(xy + yz + zx)
(xy + yz + zx) = -18
x3 + y3 + z3 - 3xyz = (x + y + z){(x + y + z)2 - 3(xy + yz + zx)}
69 - 3xyz = 3 {(9) + 54}
69 - 189 = 3xyz
xyz = -40