Solve the following inequlities `(i) sqrt(x-1) lt x-3` `(ii) sqrt(x-3) gt sqrt(7-x)` `(iii) sqrt (x^(2)+4x+9) gt x +2` `(iv) 4-x lt sqrt(2x-x^(2))` `(

Monjur Alahi

Solve the following inequlities
`(i) sqrt(x-1) lt x-3` `(ii) sqrt(x-3) gt sqrt(7-x)`
`(iii) sqrt (x^(2)+4x+9) gt x +2` `(iv) 4-x lt sqrt(2x-x^(2))`
`(v) root3((x-4)(x-6)) gt 2` `(vi) sqrt(x^(2)+3x+5) lt sqrt(x^(2)+x+1)`
`(vii) sqrt((1)/(x^(2))-(3)/(x)) lt (1)/(x)-(1)/(2)` `(viii) (sqrt(2x^(2)+7x-4))/(x+4) le (1)/(2)`
`(ix) (|x+2|-|x|)/(sqrt(8-x^(3))) ge 0`


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Salim Ahmed Kawsar

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Correct Answer - `(i) (5,oo)` `(ii) (5,7]` `(iii) R` `(iv) x in phi` `(v)(-oo,2)uu(8,oo)` `(vi) (-oo,-2)` `(vii) x in (0,(1)/(3)]` `(viii) x in (-oo,-4)uu[(1)/(2),(8)/(7)]`

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