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If the sum of a number and its reciproca...

If the sum of a number and its reciprocal be 2, then the number is यदि एक संख्या और उसके व्युत्क्रम का योग 2 हो, तो वह संख्या कितनी होगी?

A

0

B

1

C

`-1`

D

`2`

Text Solution

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The correct Answer is:
To solve the problem where the sum of a number and its reciprocal equals 2, we can follow these steps: 1. **Define the variable**: Let the number be represented as \( x \). 2. **Write the equation**: According to the problem, the sum of the number and its reciprocal can be expressed as: \[ x + \frac{1}{x} = 2 \] 3. **Eliminate the fraction**: To eliminate the fraction, multiply both sides of the equation by \( x \) (assuming \( x \neq 0 \)): \[ x^2 + 1 = 2x \] 4. **Rearrange the equation**: Rearranging the equation gives us a standard quadratic form: \[ x^2 - 2x + 1 = 0 \] 5. **Factor the quadratic equation**: The quadratic can be factored as: \[ (x - 1)(x - 1) = 0 \] or simply: \[ (x - 1)^2 = 0 \] 6. **Solve for \( x \)**: Setting the factored equation to zero gives: \[ x - 1 = 0 \implies x = 1 \] 7. **Conclusion**: Therefore, the number is: \[ x = 1 \]
To solve the problem where the sum of a number and its reciprocal equals 2, we can follow these steps: 1. **Define the variable**: Let the number be represented as \( x \). 2. **Write the equation**: According to the problem, the sum of the number and its reciprocal can be expressed as: \[ x + \frac{1}{x} = 2 \] ...
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