Question

Plz answer thr ques correctly⇪​

Answer 1

Answer:

Here two QUESTIONs ANSWER are there

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Answer 2

Answer :

(iv). (2 , 3)

Solution :

• Given : (x - 1)/(x - 2) > 2 , x € R
• To find : Solution set = ?

We have ;

=> (x - 1)/(x - 2) > 2

=> (x - 1)/(x - 2) - 2 > 0

=> [ (x - 1) - 2(x - 2) ] / (x - 2) > 0

=> (x - 1 - 2x + 4) / (x - 2) > 0

=> (3 - x)/(x - 2) > 0

=> -(x - 3)/(x - 2) > 0

=> (x - 3)/(x - 2) < 0

Here ,

Two cases arises ;

1). (x - 3) > 0 and (x - 2) < 0

OR

2). (x - 3) < 0 and (x - 2) > 0

Case1 :

→ (x - 3) > 0 and (x - 2) < 0

→ x > 3 and x < 2

→ x € (3,∞) and x € (-∞,2)

→ x € (3,∞) ∩ (-∞,2)

→ x € ∅ [ °•° There exist no real number which is greater than 3 and less than 2 simultaneously . ]

OR

Case2 :

→ (x - 3) < 0 and (x - 2) > 0

→ x < 3 and x > 2

→ x € (-∞,3) and x € (2,∞)

→ x € (-∞,3) ∩ (2,∞)

→ x € (2,3)

Here ,

The solution set will be given as the union of solutions found in both cases .

Thus ,

Solution of the given inequation will be ;

→ x € ∅ U (2,3)

→ x € (2,3)

Hence ,

Solution set is (2 , 3) .