If (x-y)^3 > (x-y)^2, then which one of the following must be true ?
A) x^3 < x^5
B) x^5 < y^4
C) x^3 > y^2
D) x^5 > y^4
E) x^3 > y^3
Soln: since (x-y)^3 is greater than (x-y)^2, we can confirm the following -
a) x-y should be positive
b) x-y cannot be equal to 0
So, dividing by (x-2)^2 throughout -
=> x-y > 1
x>1+y
x is greater than y - so the answer could be any one (C,D,E). But the book says "E" (could you please explain how)
Thanks