If x + y = 25 and xy = 35, then 1/x + 1/y =?

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RRB NTPC Exam 27 Jan 2021 click here to view all questions

If x + y = 25 and xy = 35, then 1/x + 1/y =?

A$$ \frac{\sqrt{57}}{57} $$

B$$ \frac{7}{5} $$

C$$ \frac{5}{7} $$

D$$ \frac{\sqrt{75}}{75} $$

Akhilesh ? Apr 3 '25 at 21:12

correct answer is: \(\frac{5}{7}\)
Explanation: To find \( \frac{1}{x} + \frac{1}{y} \), we use the identity \( \frac{1}{x} + \frac{1}{y} = \frac{x + y}{xy} \) Given \( x + y = 25 \) and \( xy = 35 \), we substitute these values into the equation: \[ \frac{1}{x} + \frac{1}{y} = \frac{25}{35} = \frac{5}{7} \] Thus, the correct answer is \( \frac{5}{7} \)

• OPTION A: Incorrect. \( \frac{\sqrt{57}}{57} \) does not simplify to the correct value.
• OPTION B: Incorrect. \( \frac{7}{5} \) is the reciprocal of the correct answer.
• OPTION C: Correct. \( \frac{5}{7} \) matches the derived result.
• OPTION D: Incorrect. \( \frac{\sqrt{75}}{75} \) simplifies to \( \frac{\sqrt{3}}{15} \), which is not the correct value.

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correct answer is: \(\frac{5}{7}\) Explanation: To find \( \frac{1}{x} + \frac{1}{y} \), we use the identity \( \frac{1}{x} + \frac{1}{y} = \frac{x + y}{xy} \) Given \( x + y = 25 \) and \( xy = 35 \), we substitute these values into the equation: \[ \frac{1}{x} + \frac{1}{y} = \frac{25}{35} = \frac{5}{7} \] Thus, the correct answer is \( \frac{5}{7} \) OPTION A: Incorrect. \( \frac{\sqrt{57}}{57} \) does not simplify to the correct value. OPTION B: Incorrect. \( \frac{7}{5} \) is the reciprocal of the correct answer. OPTION C: Correct. \( \frac{5}{7} \) matches the derived result. OPTION D: Incorrect. \( \frac{\sqrt{75}}{75} \) simplifies to \( \frac{\sqrt{3}}{15} \), which is not the correct value. Akhilesh ? answered Apr 3 '25 at 21:12

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