If x + y + z = 8, and x2 + y2 + z2 = 20 then the value of x3 + y3 + z3 − 3xyz is ________.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. -16.
Given that
If x + y + z = 8, and x2 + y2 + z2 = 20,
We know that,
⇒ x3 + y3 + z3 − 3xyz = 1/2 × (x + y + z) × [3(x2 + y2 + z2) - (x + y + z)2]
Now,
⇒ x3 + y3 + z3 − 3xyz = 1/2 × 8 × [3 × 20 - 82]
⇒ 4 × (60 - 64) = 4 × -4 = -16