# Which are the points from plane xoy for the relation x^2 - y^2 = x-y, to be true ?

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Student Comments

giorgiana1976 | Student

Let’s analyze the relationship given in enunciation:

x^2 – y^2=x-y

Let's express the difference of squares, x^2 – y^2 =( x-y)*(x+y)

Let’s substitute the difference of squares with the specific product:

( x-y)*(x+y)=(x-y)

We’ll subtract (x-y) both sides:

( x-y)*(x+y)- (x-y)=0

We'll factorize by (x-y).

(x-y)*(x+y-1)=0

From the relation above results:

x-y=0, so x=y

or x+y-1=0. In this case, the points which belong to the line y=1-x are the points for the relation x^2 – y^2=x-y to be true.

neela | Student

To determine points that satisfy x^2-y^2 = (x-y)

Solution:

x^2-y^2 = x-y implies

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

(x+y)(x-y) - (x-y) = 0

(x-y){x+y-1} = 0

Therefore all the points in XOY plane that are on the lines

x-y = 0 , Or x+y-1 = 0

satisfies the realtion x^2-y^2 = x-y.