Question

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

Answer 1

Answer:

It is given that 3x+2y=12 and xy=6.

We find the value of 27x

3

+8y

3

as shown below:

27x

3

+8y

3

=(3x)

3

+(2y)

3

=(3x+2y)[(3x)

2

−(3x×2y)+(2y)

2

](∵a³+b³=(a+b)(a²−ab+b²))

=12[(3x)

2

−(6×xy)+(2y)

2

](∵3x+2y=12,xy=6)

=12[(3x)

2

−(6×6)+(2y)

2

]

=12[(3x)

2

−36+(2y)

2

]

=12[(3x)

2

+(2y)

2

+(2×3x×2y)−(2×3x×2y)−36]

=12[(3x+2y)

2

−12xy−36]

=12[(12)

2

−(12×6)−36]

=12(144−72−36)

=12(144−108)

=12×36

=432

Hence, 27x

3

+8y

3

=432.