यदि \(x=\sqrt{5}-2\), तो \(x+\frac{1}{x}\) का मान क्या है?
If \(x=\sqrt{5}-2\), what is the value of \(x+\frac{1}{x}\)?
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{5}\)
Concept
\(\frac{1}{\sqrt{5}-2}=\sqrt{5}+2\), because (\(\sqrt{5}-2\)\(\sqrt{5}+2\)=1).
Why this answer is correct
Hence (x+\frac{1}{x}=\(\sqrt{5}-2\)+\(\sqrt{5}+2\)=2\sqrt{5}).
Exam Tip
When conjugates multiply to (1), the reciprocal is immediate. चरण 1: \(\frac{1}{\sqrt{5}-2}=\sqrt{5}+2\), क्योंकि (\(\sqrt{5}-2\)\(\sqrt{5}+2\)=1)। चरण 2: इसलिए (x+\frac{1}{x}=\(\sqrt{5}-2\)+\(\sqrt{5}+2\)=2\sqrt{5})। चरण 3: जहाँ संयुग्मी गुणन (1) दे, वहाँ व्युत्क्रम तुरंत मिल जाता है।
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