Using properties of determinants, solve the following for x: `|x-2 2x-3 3x-4x-4 2x-9 3x-16 x-8 2x-27 3x-64|=0`

Explanation

`Delta =|{:(x-2,,2x-3,,3x-4),(x-4,,2x-9,,3x-16),(x-8,,2x-27,,3x-64):}|=0`
Applying `R_(2) to R_(2) " and " R_(3) to R_(3) to R_(3) -R_(1)` we get
`" or " Delta = |{:(x-2,,2x-3,,3x-4),(-2,,-6,,-12),(-6,,-24,,-60):}|=0`
` rArr |{:(x-2,,2x-3,,3x-4),(1,,3,,6),(1,,4,,10):}|=0`
(Taking -2 and -6 common from`R_(2) " and "R_(3)` respectively)
`rArr (x-2). 6 - (2x-3). 4 + (3x-4).1=0`
`" or " x=4`