Question

2X-3Y=10,XY=16;Find 8Xcube-27Ycube,using identity=Xcube-Ycube-3×XY(X-Y).​

Answer 1

Answer:

hope it's helpful to you..

Answer 2

Answer:

The value of 8x³ - 27y³ is 3880.

Step-by-step-explanation:

We have given that,

• 2x - 3y = 10

• xy = 16

We have to find the value of 8x³ - 27y³.

We know that,

x³ - y³ = ( x - y ) ( x² + xy + y² )

Now, let

P = 8x³ - 27y³

⇒ P = ( 2x )³ - ( 3y )³

⇒ P = ( 2x - 3y ) [ ( 2x )² + ( 2x * 3y ) + ( 3y )² ]

⇒ P = 10 [ ( 2x )² + ( 3y )² + ( 3 * 2 * xy ) ]

⇒ P = 10 [ ( 2x )² + ( 3y )² + ( 6 * xy ) ]

⇒ P = 10 [ ( 2x )² + ( 3y )² + ( 6 * 16 ) ]

⇒ P = 10 [ ( 2x )² + ( 3y )² + 96 ]

We know that,

a² + b² = ( a - b )² + 2ab

⇒ P = 10 [ ( 2x - 3y )² + ( 2 * 2x * 3y ) + 96 ]

⇒ P = 10 [ ( 10 )² + ( 2 * 2 * 3 * xy ) + 96 ]

⇒ P = 10 [ 100 + ( 12 * 16 ) + 96 ]

⇒ P = 10 ( 100 + 192 + 96 )

⇒ P = 10 ( 292 + 96 )

⇒ P = 10 * 388

⇒ P = 3880

∴ 8x³ - 27y³ = 3880

∴ The value of 8x³ - 27y³ is 3880.