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Solve the following quadratic equation by factorization method
1/a+b+c = 1/a + 1/b + 1/c , a+b not = to 0?
1/a+b+c = 1/a + 1/b + 1/c , a+b not = to 0?
Most Upvoted Answer
Solve the following quadratic equation by factorization method1/a+b+c ...
Understanding the Equation
The equation given is:
1/a + b + c = 1/a + 1/b + 1/c
This can be simplified to find a common expression.
Rearranging the Equation
- Start by eliminating the common term on both sides:
1/a + b + c - (1/a + 1/b + 1/c) = 0
- This simplifies to:
b + c - (1/b + 1/c) = 0
Finding a Common Denominator
- Multiply through by abc to eliminate the denominators:
abc(b + c) - ac - ab = 0
- This can be rewritten as:
abc(b + c) = ac + ab
Factoring the Equation
- The expression can be factored as follows:
abc(b + c) - ab - ac = 0
=> ab(c - 1) + ac(b - 1) = 0
- This indicates either:
1. ab = 0 (which is not allowed, since a + b ≠ 0)
2. c - 1 = 0 or b - 1 = 0
Finding Solutions
- If c - 1 = 0, then c = 1
- If b - 1 = 0, then b = 1
Conclusion
The values of b and c can be determined from the equation. The assumption that a + b is not equal to 0 ensures that neither variable is zero, thus allowing for valid solutions.
This factorization method provides a systematic approach to solving the quadratic equation while ensuring clarity and correctness in the calculation process.
The equation given is:
1/a + b + c = 1/a + 1/b + 1/c
This can be simplified to find a common expression.
Rearranging the Equation
- Start by eliminating the common term on both sides:
1/a + b + c - (1/a + 1/b + 1/c) = 0
- This simplifies to:
b + c - (1/b + 1/c) = 0
Finding a Common Denominator
- Multiply through by abc to eliminate the denominators:
abc(b + c) - ac - ab = 0
- This can be rewritten as:
abc(b + c) = ac + ab
Factoring the Equation
- The expression can be factored as follows:
abc(b + c) - ab - ac = 0
=> ab(c - 1) + ac(b - 1) = 0
- This indicates either:
1. ab = 0 (which is not allowed, since a + b ≠ 0)
2. c - 1 = 0 or b - 1 = 0
Finding Solutions
- If c - 1 = 0, then c = 1
- If b - 1 = 0, then b = 1
Conclusion
The values of b and c can be determined from the equation. The assumption that a + b is not equal to 0 ensures that neither variable is zero, thus allowing for valid solutions.
This factorization method provides a systematic approach to solving the quadratic equation while ensuring clarity and correctness in the calculation process.
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Solve the following quadratic equation by factorization method1/a+b+c = 1/a + 1/b + 1/c , a+b not = to 0?
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Solve the following quadratic equation by factorization method1/a+b+c = 1/a + 1/b + 1/c , a+b not = to 0? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Solve the following quadratic equation by factorization method1/a+b+c = 1/a + 1/b + 1/c , a+b not = to 0? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Solve the following quadratic equation by factorization method1/a+b+c = 1/a + 1/b + 1/c , a+b not = to 0?.
Solve the following quadratic equation by factorization method1/a+b+c = 1/a + 1/b + 1/c , a+b not = to 0? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Solve the following quadratic equation by factorization method1/a+b+c = 1/a + 1/b + 1/c , a+b not = to 0? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Solve the following quadratic equation by factorization method1/a+b+c = 1/a + 1/b + 1/c , a+b not = to 0?.
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