Question

Solve the following Inequalities :
1. (x - 1)(3 - x)(x - 2)2 > 0​

Answer 1

Step-by-step explanation:

let A=(x-1). B=(3-x). C=(x-2)

ABC>0

multiplying first two terms

(3x-x²-3+x)(x-2)>0

now,

4x-x²-3>0. or x-2>0

x>2

4x-x²-3>0 or x²-4x+3<0

x2-3x-x+3<0

x(x-3)-1(x-3)<0

(x-1)(x-3)<0

x-1<0 or x<1

x-3<0 or x<3