Question

The ratio of two numbers is 1 to 2 and the sum of their squares is 20. Find the numbers. If there is more than one pair, use the

Answer 1

The two numbers are 2 and 4 "or" -2 and -4

Step-by-step explanation:

The given is:

• The ratio of two numbers is 1 to 2
• The sum of their squares is 20

We need to find the numbers

Assume that the smaller number is x

∵ The ratio between the two numbers is 1 : 2

∵ The smaller one is x

By using the ratio method

→  1st    :    2nd

→   1      :    2

→   x     :     ?

By using cross multiplication

∴ 1 × ? = x × 2

∴ ? = 2x

∴ The 2nd number is 2x

∵ The sum of their squares = 20

∵ Square x = x × x = x²

∵ Square (2x) = 2x × 2x = 4x²

∴ The sum of their squares = x² + 4x² = 5x²

- Equate the sum of their squares by 20

∴ 5x² = 20

- Divide both sides by 5

∴ x² = 4

- Take √ for both sides

∴ x = ± 2

∴ The smaller number is 2 OR -2

∵ The larger number is 2x

∴ 2x = 2(±2) = ± 4

∴ The larger number is 4 OR -4

The two numbers are 2 and 4 "or" -2 and -4

Learn more:

You can learn more about the ratio in brainly.com/question/2707032

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