Question

If x+y=7/13 and x-y=1/91, what is the value of x²-y²? Express your answer as a common fraction.

Answer 1

`(1)/(169)`

Explanation:

It is given:

`x+y=(7)/(13)`

and

`x-y=(1)/(91)`

We are asked to find the value of "
`x^2-y^2`"

We remember a rule/formula from algebra:

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

Using this formula we can write:

`x^2-y^2=(x+y)(x-y)=((7)/(13))((1)/(91))=(1)/(13)*(1)/(13)=(1)/(169)`

The answer is:

`(1)/(169)`