The value of x for which `|{:(x,2,2),(3,x,2),(3,3,x):}|+|{:(1-x,2,4),(2,4-x,8),(4,8,16-x):}|gt33` is

Options

A. `0ltxlt1`
B. `-(1)/(2)ltxlt(1)/(2)`
C. `xlt-(1)/(7)`
D. `xgt1`

Answer

C, D

Explanation

`|{:(x,2,2),(3,x,2),(3,3,x):}|+|{:(1-x,2,4),(2,4-x,8),(4,8,16-x):}|ge33`
`implies21x^(2)-18x+30ge33`
`implies21x^(2)-18x-3ge0`
`implies7x^(2)-6x-1ge0`
`implies7x^(2)-7x+x-1ge0`
`(7x+1)(x-1)ge0`
`impliesx in (-infty,(-1)/(7))cup(1,infty)`