Q. 414.5( 2 Votes )

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

B. 207

C. 669

D. 729

Answer :

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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