Show that the inequality x^4 < 8x^2 + 9 is satisfied for when -3 < x < 3 .

(x^2 - 9)(x^2 + 1) < 0 solving the equation to get solutions to the equality (x^2 - 9)(x^2 + 1) = 0 : x = +/- 3 or x = +/- 1 now consider points either side of these x-intercepts... for x>3: equality is not satisfied for 1<x<3: equality is satisfied for -1<x<1: equality is satisfied for -3<x<-1: equality is satisfied for x<-3: equality is not satisfied