If x + y + z = 18, xyz = 81 and xy + yz + zx = 90, then find the value of \(\sqrt[4]{x^3+y^3+z^3+xyz}\)
Answer & explanation
Correct answer: option 1
x3 + y3 + z3 - 3xyz = (x + y + z)[(x + y + z)2 - 3(xy + yz + za)]
= x3 + y3 + z3 - 3 × 81 = 18[(18)2 - 3 × 90]
= x3 + y3 + z3 - 243 = 18[324 - 270]
= x3 + y3 + z3 = 18 × 54 + 243 = 1215
The value of \(\sqrt[4]{x^3+y^3+z^3+xyz}\) = \(\sqrt[4]{1215 + 81}\) = 6