AP EAMCET · Maths · Basic of Mathematics
If \(m n=3\) and \(\frac{1}{m}+\frac{1}{n}=\frac{4}{3}\), then the value of \(0.1+0.1^{\frac{1}{m}}+0.1^{\frac{1}{n}}\) is
- A \(0.2+0.1^{\frac{1}{3}}\)
- B \(0.1+0.1^{\frac{1}{3}}+0.1^{\frac{1}{2}}\)
- C \(0.1+0.1^{\frac{4}{3}}+0.1^{\frac{1}{2}}\)
- D \(0.1+0.1^{\frac{1}{4}}+0.1^{\frac{1}{2}}\)
Answer & Solution
Correct Answer
(A) \(0.2+0.1^{\frac{1}{3}}\)
Step-by-step Solution
Detailed explanation
We have, \(m n=3\) and \(\frac{1}{m}+\frac{1}{n}=\frac{4}{3}\) \(\begin{aligned} & \Rightarrow \quad m n=3 \text { and } \frac{m+n}{m n}=\frac{4}{3} \\ & \Rightarrow \quad m n=3 \text { and } m+n=4\end{aligned}\) Solving, we get \(m=1, n=3\) or \(m=3, n=1\) Now,…
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