Find all the possible values of the expression `sqrt(x^2-4)`.

Explanation

`sqrt(x^2-4)`
Least value of square root is 0 when `x^2=4 of x= pm 2 " Also " x^2-4 ge 0 `
Hence `sqrt(x^2-4)in [ 0 oo).`
(ii) `sqrt(9-x^2)`
Least value of square root is 0 when `9-x^2=0 or x = pm 3`
Also , the least value of `9- x^2` is 9 when x=0 ltbr gt Hence , we have `0 le 9-x^2 le 9 rArr sqrt(9 - x^2) in [ 0, 3]`
(iii) `sqrt(x^2 -2 x + 10 ) = sqrt((x-1)^2+9 ge 3 `
Here the least value of `sqrt((x-1)^2+9)` is 3, when x-1 =0
Also` (x-1)^2+9 ge 9 rArr sqrt((x-1)^2+9 ge 3`
Hence `sqrt(x^2-2x+10) in [3, oo)`