1.

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?1. 9 ∶ 12. 1 ∶ 93. 9 ∶ 54. 4 ∶ 5

Answer» Correct Answer - Option 1 : 9 ∶ 1

Given:

Let the numbers be ‘x’ and ‘y’

∴ x × y = 20

x2 + y2 = 41

Formula used:

(x – y)2 = x2 + y2 – 2xy

(x + y)2 = x2 + y2 + 2xy

Calculation:

∵ (x – y)2 = x2 + y2 – 2xy

⇒ (x – y)2 = 41 – (2 × 20)

⇒ (x – y)2 = 41 – 40

⇒ (x – y)2 = 1

⇒ x – y = 1      ----(1)

∵ (x + y)2 = x2 + y2 + 2xy

⇒ (x + y)2 = 41 + (2 × 20)

⇒ (x + y)2 = 41 + 40

⇒ (x + y)2 = 81

⇒ x + y = √81 = 9      ----(2)

∴ (x + y) ∶ (x – y) = 9 ∶ 1


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