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If 3x − 2y = 11 and xy = 12, find the value of 27x3 − 8y3 - Mathematics

Answer in Brief

If 3x − 2y = 11 and xy = 12, find the value of 27x3 − 8y3

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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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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 4 Algebraic Identities
Exercise 4.3 | Q 10 | Page 20
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