If $x+y+z=7, x^2+y^2+z^2=85$ and $x^3+y^3+z^3=913$, then the value of $\sqrt[3]{x y z}$ is:
Answer & explanation
Correct answer: option 3
x3 + y3 + z3 – 3xyz = (x + y + z) (x2 + y2 + z2 – (xy + yz + zx))
(x + y + z)2 = x2 + y2 + z2 + 2(xy + yz + zx)
x + y + z = 7
x2 + y2 + z2 = 85
x3 + y3 + z3 = 913
= 72 = 85 + 2(xy + yz + zx)
= 49 – 85 = 2(xy + yz + zx)
= -36 = 2(xy + yz + zx)
= (xy + yz + zx) =-18
= 913 – 3xyz = 7(85 + 18)
= 913 – 7 × 103 = 3xyz
= 913 – 721 = 3xyz
= 192 = 3xyz
= 64 = xyz
$\sqrt[3]{x y z}$ = 4