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Find the Value of 27x3 + 8y3, If 3x + 2y = 14 and Xy = 8 - Mathematics

Answer in Brief

Find the value of 27x3 + 8y3, if 3x + 2y = 14 and xy = 8

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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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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 4 Algebraic Identities
Exercise 4.3 | Q 14.1 | Page 20
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