Question

Plz answer thr ques correctly⇪​

Answer 1

Answer :

(ii). 3

Solution :

• Given : y = √(5 - x) / (x - 3) + 1/√(x - 1)
• To find : No. of integral solutions

Here ,

y = √(5 - x) / (x - 3) + 1/√(x - 1)

The conditions for y to be a real valued function will be ;

• 5 - x ≥ 0 , x € I

• x - 3 ≠ 0 , x € I

• x - 1 > 0 , x € I

Now ,

• 5 - x ≥ 0 , x € I

→ 5 ≥ x , x € I

→ x ≤ 5 , x € I

→ x € { . . . , -1 , 0 , 1 , 2 , 3 , 4 , 5 }

• If x - 3 ≠ 0 , x € I

→ x ≠ 3 , x € I

→ x € I - {3}

→ x € { . . . - 3 , -2 , -1 , 0 , 1 , 2 , 4 , 5 . . . }

• x - 1 > 0 , x € I

→ x > 1 , x € I

→ x € { 2 , 3 , 4 , 5 . . . }

Clearly ,

The integers satisfying all the conditions are ;

2 , 4 , 5 .

Hence ,

The number of Integral solutions of the given inequation is 3 .