Find all the possible the value of the following expression`dot`
`sqrt(x^2-4)`
(ii) `sqrt(9-x^2)`
(iii) `sqrt(x^2-2x+10)`
Text Solution
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`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)`
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