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 \(x=y+1\)

Statement 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)

\(x(x-y-1)=0\)

The 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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