Question

If x + y = `5/2` and xy = 1, find x − y.

Answer 1

Here, x + y = `5/2`, xy = 1,

Thus,

`(5/2)^2 - (x-y)^2 = 4 xx 11`   ...`["Using"  (x+y)^2-(x-y)^2=4xy]`

`25/4 - (x - y)^2` = 4

∴ `(x - y)^2 = 25/4 - 4`

∴ `(x - y)^2 = (25 - 16)/4`

∴ `(x - y)^2 = 9/4`

∴ `(x - y) = ± sqrt(9/4)`

∴ `(x - y) = ± 3/2`