question_answer

The minimum value of the expression \[a+\frac{1}{a}>0\]is:

A)  0                                

B)  1

C)  2                    

D)  4

Correct Answer: C

Solution :

(c): Let \[t=a+\frac{1}{a}\]        ????????(i)

a	1/a	a+1/a
1	1	2
2	1/2	2.5
3	1/3	3.33
4	1/4	4.25
5	1/5	5.20
1/2	2	2.5
1/3	3	3.33
1/4	4	4.25

See the graph of \[y=x+\frac{1}{x},\] as shown above. Here, \[x=a\Rightarrow y=x+\frac{1}{x}=a+\frac{1}{a}\] As we can see from the table, the value of \[a+\frac{1}{a}\] is minimum when a = 1 and this a minimum value = 2