If x + y + z = 18, xyz = 81 and xy + yz + zx = 90, then find the value of 
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Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 6
x + y + z = 18
Square on both sides
x2 + y2 + z2 + 2 (xy + yz + zx) = 324
x2 + y2 + z2 + 2 (90) = 324
x2 + y2 + z2 = 324 - 180 = 144
x3 + y3 + z3 - 3xyz = (x + y + z) (x2 + y2 + z2 - (xy + yz + zx))
x3 + y3 + z3 - 3 × 81 = 18 (144 - 90)
x3 + y3 + z3 = 1215
So, the value of = (1215 + 81)1/4 = 12961/4 = (64)1/4 = 6