If x = √7 , determine the value of x + 1/x .

Question

If x = √7 , determine the value of x + 1/x .

1. A. 8√7/7 (Correct answer)
2. B. 7√7/8
3. C. 7√7/9
4. D. 9√7/7

Correct Answer

Option A — 8√7/7

Detailed Solution & Explanation

The correct answer is 8√7/7.

Key Points

• Substitute directly: $x + \dfrac{1}{x} = \sqrt{7} + \dfrac{1}{\sqrt{7}}$.
• Rationalise the second term: $\dfrac{1}{\sqrt{7}} = \dfrac{\sqrt{7}}{7}$.
• So the sum is $\sqrt{7} + \dfrac{\sqrt{7}}{7} = \dfrac{7\sqrt{7} + \sqrt{7}}{7} = \dfrac{8\sqrt{7}}{7}$.

Additional Information

• Rationalising the denominator — multiplying above and below by $\sqrt{7}$ — is what lets the two terms be added.
• A numeric check: $\sqrt{7} \approx 2.646$, so the sum is about 3.024, and $8\sqrt{7}/7 \approx 3.024$ ✓
• The related identity worth carrying: $\left(x + \tfrac{1}{x}\right)^2 = x^2 + \tfrac{1}{x^2} + 2$.

प्रश्न (हिन्दी में)

यदि x = √7 , तो x + 1/x का मान ज्ञात कीजिए।

1. A. 8√7/7
2. B. 7√7/8
3. C. 7√7/9
4. D. 9√7/7