Question

Find the value of 27 x+8yº, if
(a) 3x +2y =14 and xy = 8
14​

Answer 1

Step-by-step explanation:

Using identity:-

(3x + 2y)^{3} = 27x^{3} + 8y^{3} + (3*3x*2y)(3x +2y)(3x+2y)

3

=27x

3

+8y

3

+(3∗3x∗2y)(3x+2y)

14^{3} = 27x^{3} + 8y^{3} + (18*14*8)14

3

=27x

3

+8y

3

+(18∗14∗8)

2744 = 27x^{3} + 8y^{3} + 20162744=27x

3

+8y

3

+2016

728 = 27x^{3} + 8y^{3}728=27x

3

+8y

3

Answer 2

In the given problem,we have to find the value of

27x^2 + 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) = a^3 + b^3 + 3ab(a+b)

27x^3+8y^3+18(xy)(3x+2y)=

27x^3+8y^3+18(4)(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

Hope this helps you....