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Re: If (x-y)^3 > (x-y)^2, then which of the following must be true?
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29 Apr 2017, 23:04

1

(x-y)^3 will be positive if i) both x and y are +ve and x>y, ii) both x and y are -ve and y<x iii) x is +ve and y is -ve

Case i-Let's assume that both X&Y are positive numbers. x=3 and y=1 (x-y)^3 > (x-y)^2 Checking validity of the given options a) x^3 < y^2 Incorrect. b) x^5 < y^4 Incorrect. c) x^3 >y^2 Correct. d) x^5 > y^4 Correct. e) x^3 > y^3 Correct.

Case ii-Let's assume that both X&Y are negative numbers and y<x x=-2 and y=-5 (x-y)^3 > (x-y)^2 Checking validity of the given options a) x^3 < y^2 Correct. b) x^5 < y^4 Correct. c) x^3 >y^2 Incorrect. d) x^5 > y^4 Incorrect. e) x^3 > y^3 Correct.

Case iii-Let's assume that both X is +ve and y is -ve x=3 and y=-1 (x-y)^3 > (x-y)^2 Checking validity of the given options a) x^3 < y^2 Incorrect. b) x^5 < y^4 Incorrect. c) x^3 >y^2 Correct. d) x^5 > y^4 Correct. e) x^3 > y^3 Correct.

Re: If (x-y)^3 > (x-y)^2, then which of the following must be true?
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29 Aug 2017, 14:56

If (x−y)^3>(x−y)^2, then which of the following must be true?

Let (x−y) = a

so , a^3> a^2 implies a>0

that is x-y>0 , so that means x>y (but we cannot say for sure if x, y is >or< 0) Also X can be integers and or fractions . Don't assume that its only integer.

Now if we see all options we have

A. x^3<y^2 ( Not always true )

B. x^5<y^4 ( Not always true )

C. x^3>y^2 ( Not always true)

D. x^5>y^4 ( Not always true)

E. x^3>y^3 Yes ( true even in case of fractions)
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