Question

If x-y=4 and xy = 2, then find the value of x^3 - y^3​

Answer 1

Solution:-

Given:-

=> x - y = 4

=> xy = 2

To find

=> x³ - y³

Use this identity

=> ( x - y )³ = x³ - y³ - 3xy (x - y )

Now put the value

=> (4)³ = x³ - y³ - 3 × 2 ( 4 )

=> 64 = x³ - y³ - 6 × 4

=> 64 = x³ - y³ - 24

=> 64 + 24 = x³ - y³

=> 88 = x³ - y³

Answer

=> value of x³ - y³ is 88

Some more identities

=> a³ + b³ = (a + b )³ - 3ab( a + b )

=> a² - b² = ( a - b )( a + b )

=> ( a + b )² = a² + b² + 2ab

=> ( a - b )² = a² + b² - 2ab

=> a³ - b³ = (a - b )³ + 3ab( a - b )

=> ( a + b )³ = a³ + b³ + 3ab( a + b )

=> ( a - b )³ = a³ - b³ - 3ab(a - b )

Answer 2

Step-by-step explanation:

refer to the attachment for the explanation