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The difference of two positive integer is 3 and the sum of their squares is 89. the integers are?
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The difference of two positive integer is 3 and the sum of their squar...
Given Information:
- Difference of two positive integers: 3
- Sum of their squares: 89
Finding the Integers:
1. Let's assume the two positive integers are x and y.
2. According to the given information, we can form two equations:
- x - y = 3 (equation 1)
- x^2 + y^2 = 89 (equation 2)
3. From equation 1, we can express x in terms of y as x = y + 3.
4. Substitute x = y + 3 into equation 2:
- (y + 3)^2 + y^2 = 89
- y^2 + 6y + 9 + y^2 = 89
- 2y^2 + 6y - 80 = 0
- y^2 + 3y - 40 = 0
- (y + 8)(y - 5) = 0
5. So, the possible values for y are 5 and -8. Since the integers are positive, y = 5.
6. Substitute y = 5 back into x = y + 3 to find x:
- x = 5 + 3
- x = 8
Therefore, the two positive integers are:
- x = 8
- y = 5
- Difference of two positive integers: 3
- Sum of their squares: 89
Finding the Integers:
1. Let's assume the two positive integers are x and y.
2. According to the given information, we can form two equations:
- x - y = 3 (equation 1)
- x^2 + y^2 = 89 (equation 2)
3. From equation 1, we can express x in terms of y as x = y + 3.
4. Substitute x = y + 3 into equation 2:
- (y + 3)^2 + y^2 = 89
- y^2 + 6y + 9 + y^2 = 89
- 2y^2 + 6y - 80 = 0
- y^2 + 3y - 40 = 0
- (y + 8)(y - 5) = 0
5. So, the possible values for y are 5 and -8. Since the integers are positive, y = 5.
6. Substitute y = 5 back into x = y + 3 to find x:
- x = 5 + 3
- x = 8
Therefore, the two positive integers are:
- x = 8
- y = 5
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The difference of two positive integer is 3 and the sum of their squares is 89. the integers are?
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The difference of two positive integer is 3 and the sum of their squares is 89. the integers are? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The difference of two positive integer is 3 and the sum of their squares is 89. the integers are? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The difference of two positive integer is 3 and the sum of their squares is 89. the integers are?.
The difference of two positive integer is 3 and the sum of their squares is 89. the integers are? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The difference of two positive integer is 3 and the sum of their squares is 89. the integers are? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The difference of two positive integer is 3 and the sum of their squares is 89. the integers are?.
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