Question

x-y= 6 and xy = 10 , find the value of x cube - y cube

Answer 1

Given (x + y) = 12 and xy = 27
Recall, x3 + y3 = (x + y)3 – 3xy(x + y)
⇒ x3 + y3 = (12)3 – 3(27)(12)   = 1728 – 972
∴ x3 + y3 = 756............

Answer 2

Given :
x-y =6

Taking cube on both sides , we get

(x-y)³ = 6³

x³-y³-3x²y+3xy² = 216

x³-y³-3xy (x-y) = 216

x³-y³ - 3xy (6) = 216 (x-y = 6)

x³-y³ -3 × 10 (6) = 216 (xy = 10)

x³-y³ -180 = 216

x³-y³ = 216+180 = 396

The required value of x³-y³ = 396