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 <em>OR</em> -2
∵ The larger number is 2x
∴ 2x = 2(±2) = ± 4
∴ The larger number is 4 <em>OR</em> -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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