Question : If the sum of a number and its reciprocal is 2. Then the number is:
Option 1: 0
Option 2: 1
Option 3: –1
Option 4: 2
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Correct Answer: 1
Solution :
Given: Sum of a number and its reciprocal is 2
Let the first and second numbers be $x$ and $\frac{1}{x}$.
$x+\frac{1}{x} =2$
⇒ $(x+\frac{1}{x}) ^{2}=2^{2}$
⇒ $x^{2}+\frac{1}{x^{2}}+2= 4$
⇒ $x^{2}+\frac{1}{x^{2}} = 2$
⇒ $x^{2}+\frac{1}{x^{2}} –2=0$
⇒ $(x-\frac{1}{x}) ^{2}=0$
⇒ $x^{2}=1$
$\therefore x=1$
Hence, the correct answer is 1.
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