If the product of two numbers is 20 and sum of their squares is 41, then find…
2025
If the product of two numbers is 20 and sum of their squares is 41, then find the ratio of the sum and the difference of the two numbers?
- A.
9 ∶ 1
- B.
1 ∶ 9
- C.
9 ∶ 5
- D.
4 ∶ 5
Attempted by 26 students.
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Correct answer: A
Given: x·y = 20 and x² + y² = 41
Compute the difference and sum:
(x - y)² = x² + y² - 2xy = 41 - 40 = 1, so x - y = ±1.
(x + y)² = x² + y² + 2xy = 41 + 40 = 81, so x + y = ±9.
Therefore (x + y)/(x - y) = (±9)/(±1) = ±9. When numerator and denominator have the same sign the ratio is 9, so taking the positive values gives the ratio 9 : 1.
Answer: 9 ∶ 1