InterviewSolution
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InterviewSolution
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If `x + y + z = 12, x^(2) + Y^(2) + z^(2) = 96` and `(1)/(x)+(1)/(x)+(1)/(z)= 36` . Then find the value `x^(3) + y^(3)+z^(3).` |
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Answer» To get the value of `x^(3)+Y^(3) + z^(3) - 3xyz` `= (x + y + z ) (x^(2)+Y^(2)+x^(2) - xy- yz - zx)` …(1) We need the value of xyz and xy + yz + zx. We have `(x + Y + z)^(2) = 144` `therefore x^(2)+y^(2)+z^(2)+2xy+2yz+2xz=144` `rArr `96 + 2(xy + yz + xz) =144 `rArr `xy+ yz+ zx = 24 Given that `(1)/(x)+(1)/(x)+(1)/(z)= 36` `therefore (xy+yz+zx)/(xyz)=36` `rArr xyz = (24)/(36)=(2)/(3)` From (1), `x^(3)+y^(3)+z^(3) - 2 = 12xx(96-24)` =864 So, `x^(3)+y^(3)+z^(3) = 866` |
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