Question

If 2x+3y=12 and xy=6, find the value of 8 x + 27 . 3 y

Answer 1

Answer:

2x+3y=12 xy=6

8x  

3

+27y  

3

 

=(2x)  

3

+(3y)  

3

 

=a  

3

+b  

3

=(a+b)(a  

2

+b  

2

−ab)

8x  

3

+27y  

3

=(2x+3y)((2x)  

2

+(3y)  

2

−(2x)(3y))

=(12)[(2+3y)  

2

−12xy−6xy]

=(12)[(12)  

2

−18(6)]

=12[144−108]

=12×36

=432.2x+3y=12 xy=6

8x  

3

+27y  

3

 

=(2x)  

3

+(3y)  

3

 

=a  

3

+b  

3

=(a+b)(a  

2

+b  

2

−ab)

8x  

3

+27y  

3

=(2x+3y)((2x)  

2

+(3y)  

2

−(2x)(3y))

=(12)[(2+3y)  

2

−12xy−6xy]

=(12)[(12)  

2

−18(6)]

=12[144−108]

=12×36

=432.