Question

If 3x - 2y =11 and xy = 12, then find the value of 27x3 - 8y3.​

Answer 1

Given

3x - 2y = 11

xy = 12

To Find

27x³ - 8y³

Now Take

27x³ - 8y³

By Simplify, we get

(3x)³ - (2y)³

Using this identities

(a - b)³ = a³ - b³ - 3ab(a - b)

Let 3x = a and 2y = b ,

we get

(3x - 2y )³ = (3x)³ - (2y)³ - 3×3x×2y(3x - 2y)

Put the value

(11)³ = (3x)³ - (2y)³ - 18xy(11)

1331 = (3x)³ - (2y)³ - 18 × 12 × 11

1331 = (3x)³ - (2y)³ - 2376

(3x)³ - (2y)³ = 1331 + 2376

(3x)³ - (2y)³ = 3707

Answer

(3x)³ - (2y)³ = 3707