Question

Plz answer thr ques correctly⇪15​

Answer 1

Answer:

ANSWER is 3 integers

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Answer 2

Answer :

(i). 5

Solution :

• Given : (x + 1)/(x² + 2) > ¼ , x € I
• To find : No. of integral solution

We have ;

=> (x + 1)/(x² + 2) > ¼

=> (x + 1)/(x² + 2) - ¼ > 0

=> [ 4(x + 1) - (x² + 2) ] / 4(x² + 2) > 0

=> (4x + 4 - x² - 2) / 4(x² + 2) > 0

=> (-x² + 4x + 2) / (x² + 2) > 0

=> -(x² - 4x - 2) / (x² + 2) > 0

=> (x² - 4x - 2) / (x² + 2) < 0

Since ,

x² + 2 is always for any value of x , thus the expression (x² - 4x - 2) / (x² + 2) to be less than zero , (x² - 4x - 2) must be less than zero .

Thus ,

x² - 4x - 2 < 0

Firstly ,

Let's find the critical points for

x² - 4x - 2 = 0 .

Now ,

=> D = b² - 4ac

=> D = (-4)² - 4•1•(-2)

=> D = 16 + 8

=> D = 24

Thus ,

=> x = (- b ± √D)/2a

=> x = [-(-4) ± √24 ] / 2•1

=> x = (4 ± 2√6)/2

=> x = 2 ± √6

Now ,

The integers lying between (2 - √6) and (2 + √6) are 0 , 1 , 2 , 3 , 4 .

Hence ,

The number of Integral solutions of the given inequation is 5 .