1.

If `9^(x+1) + (a^(2)-4a-2) 3^(x) + 1 lt 0 "for all" x in R,` thenA. `a in R`B. `a in R^(+)`C. `a in [1, oo)`D. `a in R -(2)`

Answer» Correct Answer - D
We have,
`9^(x+1) + (a^(2)-4a-2) 3^(x) + 1 lt 0 "for all" x in R,`
`rArr 9y^(2) + (a^(2)-4a-2) y+1 gt 0 "for all " y gt 0, "where" y = 3^(x)`
`rArr y(9y + (1)/(y) + a^(2) -4a-2) gt 0 "for all" y gt 0`
`rArr (3sqrt(y)-(1)/(sqrt(y)))^(2) + (a-2)^(2) gt 0 "for all" y gt 0`
`rArr a ne 2 rArr a in R -(2)`


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