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The product of two number is 12 & sum of their squares is 25 then the sum of the two number is _____?
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The product of two number is 12 & sum of their squares is 25 then the ...
Understanding the Problem
To solve for the sum of two numbers, we have the following information:
- The product of the two numbers is 12.
- The sum of their squares is 25.
Let's denote the two numbers as x and y.
Equations from the Given Information
We can derive the following equations from the problem statement:
- x * y = 12 (1)
- x² + y² = 25 (2)
Relationship Between Equations
We can use the identity that relates the sum of squares to the product and sum of the numbers:
x² + y² = (x + y)² - 2xy
Substituting the known values into this identity gives us:
25 = (x + y)² - 2(12)
Now simplifying:
25 = (x + y)² - 24
This can be rearranged to find (x + y)²:
(x + y)² = 25 + 24
(x + y)² = 49
Finding the Sum
Taking the square root of both sides, we find:
x + y = √49
x + y = 7
Conclusion
Thus, the sum of the two numbers is:
- 7
This approach effectively utilizes algebraic identities and relationships to solve the problem systematically.
To solve for the sum of two numbers, we have the following information:
- The product of the two numbers is 12.
- The sum of their squares is 25.
Let's denote the two numbers as x and y.
Equations from the Given Information
We can derive the following equations from the problem statement:
- x * y = 12 (1)
- x² + y² = 25 (2)
Relationship Between Equations
We can use the identity that relates the sum of squares to the product and sum of the numbers:
x² + y² = (x + y)² - 2xy
Substituting the known values into this identity gives us:
25 = (x + y)² - 2(12)
Now simplifying:
25 = (x + y)² - 24
This can be rearranged to find (x + y)²:
(x + y)² = 25 + 24
(x + y)² = 49
Finding the Sum
Taking the square root of both sides, we find:
x + y = √49
x + y = 7
Conclusion
Thus, the sum of the two numbers is:
- 7
This approach effectively utilizes algebraic identities and relationships to solve the problem systematically.
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The product of two number is 12 & sum of their squares is 25 then the sum of the two number is _____?
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The product of two number is 12 & sum of their squares is 25 then the sum of the two number is _____? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The product of two number is 12 & sum of their squares is 25 then the sum of the two number is _____? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The product of two number is 12 & sum of their squares is 25 then the sum of the two number is _____?.
The product of two number is 12 & sum of their squares is 25 then the sum of the two number is _____? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The product of two number is 12 & sum of their squares is 25 then the sum of the two number is _____? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The product of two number is 12 & sum of their squares is 25 then the sum of the two number is _____?.
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