Question

If x+y+z=1 ,xy+yz+zx=-1 find x^3+y^3+z^3

Answer 1

Correct Question:

If x + y + z = 1 , xy + yz + zx = -1 and xyz = -1 Find x³+y³+z³

Solution:

Given:

=> x + y + z = 1

=> xy + yz + zx = -1

=> xyz = -1

We know that,

=> x³ + y³ + z³ - 3xyz = (x + y + z)[x² + y² + z² - xy - yz - zx]

Put the following values,

=> x³ + y³ + z³ - 3(-1) = (1)[(x + y + z)² - 2(xy + yz + zx) - xy - yz - zx]

=> x³ + y² + z² + 3 = 1[1² - 3(xy + yz + zx)]

=> x³ + y³ + z³ + 3 = 1[1 - 3(-1)]

=> x³ + y³ + z³ + 3 = 1[1 + 3]

=> x³ + y³ + z³ + 3 = 4

=> x³ + y³ + z³ = 4 - 3

=> x³ + y³ + z³ = 1