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Question
Find the value of 27x3 + 8y3, if 3x + 2y = 14 and xy = 8
Solution
In the given problem, we have to find the value of `27x^3 + 8y^3`
Given `3x + 2y = 14, xy = 8`
On cubing both sides we get,
`(3x+ 2y)^3 = (14)^3`
We shall use identity `(a+b)^3 = a^3 + b^3 + 3ab(a+b)`
`27x^3 + 8y^3 + 3(3x) (2y) (3x+ 2y) = 14 xx 14 xx 14`
`27x^3 + 8y^3 +18(xy)(3x+2y) = 14 xx 14 xx 14`
`27x^3 + 8y^3 + 18(8)(14) = 2744`
`27x^3 + 8y^3 + 2016 = 2744`
` 27x^3 + 8y^3 = 2744 -2016`
`27x^3 +8y^3 = 728`
Hence the value of `27x^3 +8y^3`is 728.
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