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Question
Find the value of 27x3 + 8y3, if 3x + 2y = 20 and xy = \[\frac{14}{9}\]
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Solution
Given `3x+2y = 20,xy = 14/9`
On cubing both sides we get,
`(3x+ 2y)^3 = (20)^3`
We shall use identity `(a+b)^3 = a^3 + b^3 + 3ab(a+b)`
`27x^3 + 8y^3 + 3(3x)(2y)(3x+2y) = 20 xx 20 xx 20`
`27x^3 + 8y^3 + 18 (xy)(3x+ 2y)= 8000`
`27x^3 + 8y^3 + 18 (14/9)(20) = 8000`
` 27x^3 + 8y^3 = 8000 - 560`
`27x^3 + 8y^3 = 7440`
Hence the value of ` 27x^3 + 8y^3 `is 7440 .
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