Question

if x - y = 5 and xy = -6, find value of x^3 - y^3

Answer 1

Formula:

x³ - y³ = (x - y)(x² + y² + xy)

We also know:

(x - y)² = x² + y² - 2xy

x² + y² = (x - y)² + 2xy ----------- Sub into the formula on top

Simplify x³ - y³:

x³ - y³ = (x - y)(x² + y² + xy)

x³ - y³ = (x - y)((x - y)² + 2xy + xy)

x³ - y³ = (x - y)( (x - y)² + 3xy)

We know that x - y = 5 and xy = -6:

x³ - y³ = (5)( (5)² + 3(6))

x³ - y³ = (5) (25 + 18)

x³ - y³ = (5) (43)

x³ - y³ = 215

Answer: 215