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Find two numbers such that their sum is 6 and the product is 14?
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Find two numbers such that their sum is 6 and the product is 14?
Finding Two Numbers
Let's denote the two numbers as x and y. We are given that:
Sum of the numbers:
- x + y = 6
Product of the numbers:
- x * y = 14
Solving the Equations
We can use the given information to form two equations:
- From the first equation, we get y = 6 - x
- Substitute y in the second equation:
- x * (6 - x) = 14
- Expand the equation:
- 6x - x^2 = 14
- Rearrange the terms:
- x^2 - 6x + 14 = 0
- Using the quadratic formula, we find two possible values of x:
- x = (6 ± √(6^2 - 4*1*14)) / 2
- x = (6 ± √(36 - 56)) / 2
- x = (6 ± √(-20)) / 2
- x = (6 ± 2i√5) / 2
- x = 3 ± i√5
Final Result
Therefore, the two numbers that satisfy the given conditions are:
- x = 3 + i√5
- y = 3 - i√5
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Find two numbers such that their sum is 6 and the product is 14?
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Find two numbers such that their sum is 6 and the product is 14? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Find two numbers such that their sum is 6 and the product is 14? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find two numbers such that their sum is 6 and the product is 14?.
Find two numbers such that their sum is 6 and the product is 14? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Find two numbers such that their sum is 6 and the product is 14? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find two numbers such that their sum is 6 and the product is 14?.
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