Solve the equation `(12x-1)(6x-1)(4x-1)(3x-1)=5`

Explanation

The given equation can be written as
`(x-1/12)(x-1/16)(x-1/4)(x-1/3)=5/(12.6.4.3)`……………..i
Since `1/12lt 1/6 lt 1/4 lt 1/3` and `1/6-1/12=1/3-1/4`
We can introduced a new variable
`y=1/4[(x-1/12)+(x-1/6)+(x-1/4)+(x-1/3)]`
`y=x-5/24`
On substituting `x=y+5/24` in Eq. (i) we get
`(y+3/24)(y+1/24)(y-1/24)(y-3/24)=5/(12.6.4..3)`
`implies[y^(2)-(1/24)^(2)][y^(2)-(3/24)^(2)]=5/(12.6.4.3)`
Hence we find that
`y^(2)=49/(24^(2))`
i.e.`y_(1)=7/24` and `y_(2)=-7/24`
Hence the corresponding roots of the original equation are `-1/12` and `1/2`.