# Find the Value of 27x3 + 8y3, If 3x + 2y = 20 and Xy = 14 9 - Mathematics

Find the value of 27x3 + 8y3, if  3x + 2y = 20 and xy = $\frac{14}{9}$

#### 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 .

Concept: Algebraic Identities
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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 4 Algebraic Identities
Exercise 4.3 | Q 14.2 | Page 20

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