Find the compound ratio of the ratios ` (x + y) : (x - y), (x^(2) + y^(2)) : (x + y)^(2) " and " (x^(2)-y^(2))^(2) : (x^(4) - y^(4))`.

Explanation

The compound ratio of the ratios
`(x+ y) : (x - y), (x^(2) + y^(2)) " and " (x^(2) - y^(2)) : (x^(4) - y^(4))`
` = (x + y) (x^(2) + y^(2))(x^(2) - y^(2)) : (x-y) (x + y)^(2) (x^(4) -y^(4))`
`=((x+y)(x^(2)+y^(2))(x^(2)-y^(2))^(2))/((x-y)(x+y)^(2)(x^(4)-y^(4)))`
`= ((x+y)(x^(2)+y^(2)){(x+y)(x-y)}^(2))/((x-y)(x+y)^(2)(x^(2)+y^(2))(x^(2)-y^(2)))`
` = ((x+y)^(2)(x-y)^(2))/((x-y)(x+y)(x^(2)-y^(2)))=((x+y)(x-y))/(x^(2)-y^(2))`
` = (x^(2)-y^(2))/(x^(2)-y^(2)) = 1/1 = 1 : 1 `
Hence the required compound ratio ` = 1 : 1` .