Question

Find the range of x in the equation-
(x2 - 5x + 7) / (x² - 7x + 12) < 1/2
​

Answer 1

Answer:

1<x<2

Step-by-step explanation:

$2(x^2-5x+7),x^2-7x+12\\2x^2-10x+14-x^2+7x-12<0\\\\x^2-3x+2<0\\(x-1)(x-2)<0\\When x-1=0 or x-2=0\\x=1,2$

We have 3 intervals x<1 , 1<x<2 , x>2

For interval x<1, pick x=0 then

$0^2-3(0)+2<0\\2<0$false

For interval x>2, pick x=3 then

$3^2-3(3)+2<0\\9-9+2<0\\2<0$False

Fo interval 1<x<2, pick x =1.5 then

$(1.5)^2-3(1.5)+2<0\\2.25-4.5+2<0\\-0.25<0$True

Therefore, 1<x<2