If x + y + z = 1, xy + yz + yz = –31 and x³ + y³ + z³ = 178, then what will be the value of xyz

If x + y + z = 1, xy + yz + yz = –31 and x³ + y³ + z³ = 178, then what will be the value of xyz?

(a) 25

(b) 26

(c) 27

(d) 28

Sol:

x³+y³+z³ – 3xyz = (x+y+z){(x+y+z)² – 3(xy+yz+zx)}

⇒ 178 – 3xyz = 1(1² + 93)

⇒ 3xyz = 178 – 94

⇒ xyz = 28