`(sqrt(8+2x-x^2)>6-3x)`

1.	`(sqrt(8+2x-x^2)>6-3x)`
Answer» Correct Answer - `x in (1,4]` `sqrt(8+2x-x^(2)) gt 6-3x` We must `8+2x-x^(2) ge 0` `implies x in [-2,4 ]` …….`(i)` For `6-2x lt 0` or `x gt 2` , inequality is satisfied. Let `6-3x ge 0` `implies x le 2`…….`(ii)` `implies 8+2x-x^(2) gt 36+9x^(2)-36x` `implies 5x^(2)-19x+14 lt 0` `implies (5x-14)(x-1) lt 0` `implies x in (1,(14)/(5))`.........`(iii)` From `(ii)` and `(iii)`, `x in (1,2]` `:. "finally" x in (1,4]`

Discussion

The solution of the inequality `(|x+2|-|x|)/(sqrt(8-x^(3))) ge 0` isA. `[-1,2]`B. `[1,2]`C. `[-1,1]`D. `[0,3sqrt(4))`
The number of solutions of the equation `sqrt(x^(2))-sqrt((x-1)^(2))+sqrt((x-2)^(2))=sqrt(5)` isA. `0`B. `1`C. `2`D. More than `2`
The number of integers satisfying the equation `|x|+|(4-x^(2))/(x)|=|(4)/(x)|` isA. `5`B. `4`C. `6`D. `7`
If `|(12x)/(4x^(2)+9)| le 1`, thenA. `x in R`B. `x in [-3,3]`C. `x in [-1,oo)`D. `x in (-oo,2]`
The solution of `|x+(1)/(x)| gt 2` isA. `R-{0}`B. `R-{-1,0,1}`C. `R-{1}`D. `R-{-1,1}`
The solution of `|2x-3| lt |x+2|` isA. `(-oo,1//3)`B. `(1//3,5)`C. `(5,oo)`D. `(-oo,1//3) uu (5,oo)`
Solve : `(|x-1|-3)(|x+2)-5) lt 0`.
Solve, `(1-sqrt(21-4x-x^(2)))/(x+1) ge 0`.
Solve, `(sqrt(2x-1))/(x-2) lt 1`.
`(sqrt(8+2x-x^2)>6-3x)`