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Question
If 2x+3y = 13 and xy = 6, find the value of 8x3 + 27y3
Solution
In the given problem, we have to find the value of `8x^3 + 27y^3`
Given`2x + 3y = 13, xy = 6`
In order to find `8x^3 + 27y^3`we are using identity `(a+b )^3 = a^3 + b^3 + 3ab(a+b)`
`(2x + 3y )^3 = (13)^3`
`8x^3 + 27 y^3 + 3 (2x)(3y)(2x+ 3y)= 2197`
` 8x^3 + 27y^3 + 18xy (2x+ 3y) = 2197`
Here putting, `2x + 3y = 13, xy = 6`
`8x^3 + 27y^3 + 18 xx 6 xx 13 = 2197`
` 8x^3 + 27y^3 + 1404 = 2197`
` 8x^3 + 27y^3 = 2197 - 1404`
`8x^3+ 27y^3 = 793`
Hence the value of `8x^3 + 27y^3` is 793.
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