Question

If `R_2={(x,y)| x and y` are integers and `x^2 +y^2=64`} is a relation. Then find `R_2`.

Answer 1

We have `R_(2)={(x,y)x and y` are integers and `x^(2)+y^(2)=64}`
Since, 64 is the sum of squares of `0and +-8`
When x=0 then `y^(2)=64rArry=+-8`
x =8, then `y^(2)=64-8^(2)rArr64-64=0`
x=-8, then `y^(2)=64-(-8)^(2)=64-64=0`
`:. R_(2)={(0,8),(0,-8),(8,0),(-8,0)}`