If $x + y + z = 17, xyz = 171$ and $xy + yz + 2zx = 111$,then the value of $\sqrt[3]{(x^{3}+y^{3}+z^{3}+xyz)}$ is: |
-64 4 0 -4 |
-4 |
x + y + z = 17 xy + yz + zx = 111 xyz = 171 We know that, (x + y + z)2 = x2 + y2 + z2 + 2(xy + yz + zx) = 172 = x2 + y2 + z2 + 2 × 111 = x2 + y2 + z2 = 289 – 222 = x2 + y2 + z2 = 67 We also know that, x3 + y3 + z3 – 3xyz = (x + y + z)[x2 + y2 + z2 – (xy + yz + zx)] = x3 + y3 + z3 – 3 × 171 = 17 × (67 – 111) = x3 + y3 + z3 – 513 = -748 = x3 + y3 + z3 = -748 + 513 = x3 + y3 + z3 = -235 $\sqrt[3]{(x^{3}+y^{3}+z^{3}+xyz)}$ = $\sqrt[3]{-235 +171)}$ = -4 |