Question

If x-2y=1 and xy=8 then find the value of x^3-8y^3

Answer 1

Answer:

224

Step-by-step explanation:

We have the identity a³ + b³ = (a+b)³ - 3ab (a+b) …………………………………….(1)

Rewriting, x³ + 8y³ = (x)³ + (2y)³

which is of the form a³ + b³ where a=x and b=2y.

Substituting the above values of a and b in (1),

x³ + 8y³ = (x+2y)³ - 3x.2y (x + 2y) = (x+2y)³ - 6xy (x + 2y)……………………………(2)

But we are given that x+2y = 8 and xy = 6. Substitute these values in (2) and obtain,

x³ + 8y³ = (8)³ - 6.6 (8) = 512 - 288

= 224