Question

Find x3 -y3,if x-y=5 and xy=14

Answer 1

335

Explanation:

Factor the given binomial:

x - y = 5

xy = 14

x = y + 5

(y + 5)y = 14

y^2 + 5y - 14 = 0

(y + 7)(y - 2) = 0

y = -7 or y = 2

y = -7

xy = 14

-7x = 14

x = -2

y = 2

2x = 14

x = 7

Solutions:

x = -2, y = -7

x = 7, y = 2

For x = -2, y = 7

x^3 - y^3 =

= (-2)^3 - (-7)^3

= -8 - (-343)

= 335

For x = 7, y = 2

x^3 - y^3 =

= 7^3 - 2^3

= 343 - 8

= 335