If x + y + z = 1, xy + yz + zx = -1 and xyz = -1, then (x3 + y3 + z3) is equals to:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 1.
We know that,
x3 + y3 + z3 = (x + y + z)(x2 + y2 + z2 - xy - yz - zx) + 3xyz
Given that,
x + y + z = 1
xy + yz + zx = -1 and,
xyz = -1
So,
The value of (x2 + y2 + z2) = (x + y + z)2 - 2(xy + yz + zx)
⇒ (x2 + y2 + z2) = (1)2 - 2(-1)
⇒ (x2 + y2 + z2) = 1 + 2 = 3
Now, on putting the given values
x3 + y3 + z3 = (x + y + z)(x2 + y2 + z2 - xy - yz - zx) + 3xyz
⇒ 1 × (3 - (-1)) + 3(-1)
⇒ 1 × 4 - 3
⇒ 4 - 3 = 1