असमिका `log_(sin((pi)/(3)))(x^(2)-3x+2)=2` का हल है

Explanation

`log_(sin((pi)/(3)))(x^(2)-3x+3)=2`
`rArrx^(2)-3x+2le(3)/(4)rArrx^(2)-3x+(5)/(4)le0`
`rArr" "4x^(2)-12x+5le0`
`rArr" "4x^(2)-10x-2x+5le0`
`rArr(2x-5)(2x-1)le0rArr(1)/(2)lexle(5)/(2)` . . .(i)
तथा `x^(2)-3x+2gt0rArr(x=1)(x-2)gt0`
`rArrxlt1` या `xgt2` . . . (ii)
सम्बन्ध (i) व (ii) से, `[(1)/(2),1)cup(2,(5)/(2)]`