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UPSC NDA Math Model Paper 3
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© examsnet.com
Question : 5
Total: 120
The minimum value of the expression
3
x
+
3
1
−
x
,
x
∈
R
,
is
0
1
1/3
2
√
3
Validate
Solution:
We have to find minimum value of the expression
3
x
+
3
1
−
x
We know A.M. ≥ G.M. for positive numbers.
Therefore,
3
x
+
3
1
−
x
2
≥
√
3
x
.
3
1
−
x
⇒
3
x
+
3
1
−
x
≥
2
√
3
x
+
1
−
x
⇒
3
x
+
3
1
−
x
≥
2
√
3
So, minimum value of the expression is
2
√
3
© examsnet.com
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