# If x + y + z = 9 and xy + yz + zx = 23, then the value of (x3 + y3 + z3 – 3xyz) = ?A. 108B. 207C. 669D. 729

It is given that,

x + y + z = 9

And, xy + yz + zx = 23

As we know that,

(x + y + z)2 = (x2 + y2 + z2 + 2xy + 2yz + 2zx)

(9)2 = [x2 + y2 + z2 + 2 (xy + yz + zx)]

x2 + y2 + z2 = 81 – 2 × 23

x2 + y2 + z2 = 81 – 46

x2 + y2 + z2 = 35

We also know that:

(x3 + y3 + z3 – 3xyz) = (x + y + z) [x2 + y2 + z2 – (xy + yz + zx)]

= 9 (35 – 23)

= 9 × 12

= 108

Hence, option A is correct

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