If `(x^(2) - x - 1)^(x^(2) - 7x + 12) = 1` then

Options

A. Positive integral solutions are `4`
B. Negative integral solutions are `2`
C. non positive integral solution are `2`
D. Total integral solutions are `6`

Answer

A, C, D

Explanation

`x^(2) - x- 1 = 1 rArr x^(2) - x- 2 = a`
`(x - 2)(x + 1) = 0 rArr x = 2, -1`
and `x^(2) - x- 1 = -1 rArr x = 0, 1`
at `x = 0 rarr x^(2) - 7x + 12 = 12`
`x = 1 rarr x^(2) - 7x + 12 = 6`
and `x^(2) - 7x + 12 = 0 rArr x = 4, 3`
so `x = {2, -1, 0, 1, 4, 3}`