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Sum of the two different positive integer is 11 and the sum of their square is 61. what is the ratio of these integers?
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Sum of the two different positive integer is 11 and the sum of their s...
Problem: Sum of the two different positive integer is 11 and the sum of their square is 61. What is the ratio of these integers?
Solution:
Let's assume that the two integers are x and y.
1. Formulating equations:
From the given conditions, we can form two equations:
x + y = 11 (Equation 1)
x² + y² = 61 (Equation 2)
2. Solving the equations:
We can use Equation 1 to find one of the variables in terms of the other:
x + y = 11
y = 11 - x
Substituting this expression for y in Equation 2, we get:
x² + (11 - x)² = 61
Simplifying and solving for x, we get:
x² - 11x + 20 = 0
This equation can be factored as:
(x - 5)(x - 6) = 0
So, x = 5 or x = 6.
Using Equation 1, we can find the corresponding values of y:
If x = 5, then y = 11 - x = 6.
If x = 6, then y = 11 - x = 5.
3. Calculating the ratio:
The ratio of x to y can be calculated as:
x/y = 5/6 or 6/5
So, the ratio of the two integers is either 5:6 or 6:5.
Therefore, the answer is:
The ratio of the two integers is either 5:6 or 6:5.
Solution:
Let's assume that the two integers are x and y.
1. Formulating equations:
From the given conditions, we can form two equations:
x + y = 11 (Equation 1)
x² + y² = 61 (Equation 2)
2. Solving the equations:
We can use Equation 1 to find one of the variables in terms of the other:
x + y = 11
y = 11 - x
Substituting this expression for y in Equation 2, we get:
x² + (11 - x)² = 61
Simplifying and solving for x, we get:
x² - 11x + 20 = 0
This equation can be factored as:
(x - 5)(x - 6) = 0
So, x = 5 or x = 6.
Using Equation 1, we can find the corresponding values of y:
If x = 5, then y = 11 - x = 6.
If x = 6, then y = 11 - x = 5.
3. Calculating the ratio:
The ratio of x to y can be calculated as:
x/y = 5/6 or 6/5
So, the ratio of the two integers is either 5:6 or 6:5.
Therefore, the answer is:
The ratio of the two integers is either 5:6 or 6:5.
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Sum of the two different positive integer is 11 and the sum of their square is 61. what is the ratio of these integers?
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Sum of the two different positive integer is 11 and the sum of their square is 61. what is the ratio of these integers? for CLAT 2025 is part of CLAT preparation. The Question and answers have been prepared according to the CLAT exam syllabus. Information about Sum of the two different positive integer is 11 and the sum of their square is 61. what is the ratio of these integers? covers all topics & solutions for CLAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Sum of the two different positive integer is 11 and the sum of their square is 61. what is the ratio of these integers?.
Sum of the two different positive integer is 11 and the sum of their square is 61. what is the ratio of these integers? for CLAT 2025 is part of CLAT preparation. The Question and answers have been prepared according to the CLAT exam syllabus. Information about Sum of the two different positive integer is 11 and the sum of their square is 61. what is the ratio of these integers? covers all topics & solutions for CLAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Sum of the two different positive integer is 11 and the sum of their square is 61. what is the ratio of these integers?.
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