Solve for `sin^(-1) (sin 5) gt x^(2) - 4x`

Answer

`2 0 sqrt(9 - 2pi) lt x lt 2 + sqrt(9 - 2pi)`

Explanation

We have `sin^(-1) (sin 5) gt x^(2) - 4x`
Since, `(3pi)/(2) lt 5 lt (5pi)/(2)`
`:. Sin^(-1) (sin 5) = 5 - 2pi`
`rArr 5 - 2pi gt x^(2) - 4x`
`rArr x^(2) - 4x + 4 lt 9 - 2pi`
`rArr (x - 2)^(2) lt 9 - 2pi`
rArr -sqrt(9 - 2pi) lt x x - 2 lt sqrt(9 - 2pi)`
`rArr 2- sqrt(9 - 2 pi) lt x lt 2 + sqrt(9 - 2 pi)`