Question

The minimum value of 4 + 41-2, x e R is
a 2

b 4

c 1

d 0
​

Answer 1

Answer:

option b)4 is the crt answer

Answer 2

Answer:

option b) 4 is correct

Step-by-step explanation:

The minimum value of 4x+41–x , x ∈ R, is. A) 2 B) 4 C) 1 D)0

'x' belongs to R ( the set of Real numbers)

4^x is a positive real number. And 4^(1-x) is a positive real number too.

As we know that the arithmetic mean of non negative real numbers > or = the geometric mean of the same

AM = { 4^x + 4^(1-x) } / 2

GM = √{4^x * 4^(1-x)}

So, {4^x + 4^(1-x)} /2 >, = √{4^x * 4^(1-x)}

=> 4^x + 4^(1-x)>, = 2* √4^(x+1-x)

=> 4^x + 4^(1-x) >,= 2 * √4

=> 4^x + 4^(1-x) >,= 4

Hence , minimum value is 4

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