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Question
If 3x − 2y = 11 and xy = 12, find the value of 27x3 − 8y3
Solution
In the given problem, we have to find the value of `27x^3 - 8y^3`
Given `3x- 2y= 11,xy = 12`,
In order to find `27x^3 - 8y^3`we are using identity `(a-b)^3 = a^3 - b^3 - 3ab (a-b)`
`(3x - 2y)^3 = (11)^3`
`27x^3 - 8y^3 -3 (3x)(2y)(3x- 2y) = 11 xx 11 xx 11`
`27x^3 - 8y^3 -3 (3x)(2y)(3x- 2y) = 1331`
Here putting, 3x - 2y = 11,xy= 12
`27x^3 - 8y^3 - 18 xx 12 xx 11 = 1331`
`27x^3 -8y^3 - 2376 = 1331`
`27x^3 - 8y^3 = 1331 + 2376`
`27x^3 -8y^3 = 3707`
Hence the value of `27x^3 - 8y^3`is 3707.
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