If x + y + z = 9 and xy + yz + zx = 20 find the value of x^3 + y^3 + z^3 - 3xyz

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08 Jan 2020 Solve

If x + y + z = 9 and xy + yz + zx = 20 find the value of x^3 + y^3 + z^3 - 3xyz

OPtion

1) 32
2) 49
3) 64
4) 48
5) 169
6) 181
7) 321
8) 279
9) 544
10) None of these

Solution

Given x + y + z = 9 and xy + yz + zx = 20
Consider, x + y + z = 9
Squaring on both sides, we get
(x + y + z)^2 = 9^2
x2 + y2 + z2 +2(xy + yz +zx) = 81
⇒ x2 + y2 + z2 = 81 − 2(xy + yz +zx)

=> 91 − 2(20) = 81 − 40 = 41
∴ x2 + y2 + z2 = 41
We know that x^3 + y^3 + z^3 − 3xyz = (x + y + z)( x2 + y2 + z2 − xy − yz − zx)
=> 9(41 −20) = 9(22) = 189

Correct Option: 10 Best Solution (0)