Question

find the range of x if [{(x-2)(x-4)(x-7)}/{(x+2)(x+4)(x+7)}]>1

Answer 1

(x-2)(x-4)(x-7)
------------- > 1 --- (x-2)(x-4)(x-7) > (x+2)(x+4)(x+7)
(x+2)(x+4)(x+7)

(x*2 -6x +8)(x-7) > (x*2 +6x +8)(x+7)
x*3 -7x*2 -6x*2 +42x +8x -56 > x*3 +7x*2 +6x*2 +42x +8x +56
x*3 -x*3 -7x*2 -7x*2 -6x*2 +6x*2 +42x -42x +8x -8x -56 -56 >0
-14x*2 -112 >0
-14x*2 > 112
x*2 > 112/-14
x*2 > -8
x_1,_2 > +/- 2i radical2

Answer 2

it is incorrect method

Answer 3

x_1> 2i radical 2
x_2< -2i radical 2