Question

Ex. 20. Show that the maximum value of x² – 2x+4 / x^2 + 2x + 4 is 3, for real values of x.
​

Answer 1

Answer:

Correct option is

D

3

1

and 3

Given,

3

1

<

x

2

+2x+4

x

2

−2x+4

<3 for all x∈R.

⇒

3

1

<

x

2

−2x+4

x

2

+2x+4

<3 for all x∈R. ...(1)

Let 3

x+1

=y

Then,y∈R for all x∈R.

∴

9.3

2x

−6.3

x

+4

9.3

2x

+6.3

x

+4

=

3

2x+2

−2.3

x+1

+4

3

2x+2

+2.3

x+1

+4

=

y

2

−2y+4

y

2

+2y+4

From (1),

3

1

<

y

2

−2y+4

y

2

+2y+4

<3

∴

3

1

<

9.3

2x

−6.3

x

+4

9.3

2x

+6.3

x

+4

<3.

Answer 2

Answer:

3/1 and 3 is the answer

Step-by-step explanation:

hope it helps you