x, y and z are real numbers. If x³ + y³ + z³ = 13, x + y + z = 1, and xyz = 1, then what is the value of xy + yz + zx ?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 ie -3.
x³ + y³ + z³ - 3xyz = (x + y + z)(x² + y² + z² - xy - zy - zx)
x³ + y³ + z³ - 3xyz = (x + y + z)[(x + y + z)² - 3(xy + yz + zx)]
13 - 3(1) = 1[(1)² - 3(xy + yz + zx)]
10 = 1[1 - 3(xy + yz + zx)]
xy + yz + zx = -3