Question

If x−y = 15 and xy = 20, then find the value of 1/x^3 −1/y^3 .​

Answer 1

Given : x−y = 15 and xy = 20

To Find :  1/x³ - 1/y³

Solution:

x−y = 15

Squaring both sides

( x - y)² = 15²

=> x² + y² - 2xy  = 225

=> x² + y² - 2(20) = 225

=> x² + y² = 265

1/x³ - 1/y³

= (y³ - x³)/x³y³

= ( y - x) ( y² + x²  + xy)/(xy)³

y - x= -(x-y) = -15

y² + x² = 265

xy = 20

= (-15) (265 + 20)/(20)³

= - 15(285) /20³

=  - 4,275/8000

= -171/320

= -0.534375

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