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
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