If x+y+z = 7
x2 + y2 + z2 = 85
x3 + y3 + z3 = 913
then \(\sqrt[3]{xyz}-4\) is equal to:
Answer & explanation
Correct answer: option 3
(x+y+z)2 = x2 + y2 + z2 + 2(xy +yz+zx)
49 = 85 + 2(xy +yz+zx)
xy +yz+zx = -18
x3 + y3 + z3 - 3xyz = (x+y+z) (x2 + y2 + z2 - xy - yz - zx)
913 - 3xyz = (7)(85 -(-18))
3xyz = 192
xyz = 64
\(\sqrt[3]{xyz}-4\) = \(\sqrt[3]{64}-4\) = 0