daviesj wrote:

Are the positive integers x and y consecutive?

(1)x^2 - y^2 = 2y + 1

(2) x^2 - xy - x = 0

The question is basically asking whether

x=y+1Statement 1)

x^2 - y^2=2y+1 can be written as

(x+y)(x-y)=2y+1.----equation 1

If we put

x=y+1, then LHS must be equal to RHS.

Equation 1 can be written, after substituting x=y+1, as

(2y+1)(1)=2y+1. They are equal. Hence x and y are consecutive.

Statement 2)

x(x-y-1)=0The above equation can be equal to 0 only when

x-y=1 because x is given to be positive.

Hope I am correct.

+1D

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