Question

If 5x − 4y = 6 and xy = 2, find the value of 125x³ − 64y³.

Answer 1

Here, 5x − 4y = 6 and xy = 2,

Let a = 5x, b = 4y

Using the identity:

a³ − b³ = (a − b)³ + 3ab(a − b)

(5x)³ − (4y)³ = (6)³ + 3(5x) (4y)(6)

125x³ − 64y³ = 216 + 3(20xy)(6)

125x³ − 64y³ = 216 + 3[(20)(2)](6)

125x³ − 64y³ = 216 + 3(40)(6)

125x³ − 64y³ = 216 + 3(240)

125x³ − 64y³ = 216 + 720

∴ 125x³ − 64y³ = 936