UPSC Exam > UPSC Questions > Ques4. If a - b = 3 and a2 + b2 = 29, find th...
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Ques4. If a - b = 3 and a2 + b2 = 29, find the value of ab.
A. 10
B. 12
C. 15
D. 18?
A. 10
B. 12
C. 15
D. 18?
Most Upvoted Answer
Ques4. If a - b = 3 and a2 + b2 = 29, find the value of ab.A. 10B. 12C...
Given Equations
We have two key equations:
- a - b = 3 (Equation 1)
- a² + b² = 29 (Equation 2)
Finding 'a' and 'b'
From Equation 1, we can express 'a' in terms of 'b':
- a = b + 3
Now, substitute this expression for 'a' into Equation 2:
- (b + 3)² + b² = 29
Expanding the Equation
- (b² + 6b + 9) + b² = 29
- 2b² + 6b + 9 = 29
Simplifying the Equation
- 2b² + 6b + 9 - 29 = 0
- 2b² + 6b - 20 = 0
Dividing by 2
- b² + 3b - 10 = 0
Factoring the Quadratic
- (b + 5)(b - 2) = 0
Hence, the solutions are:
- b = -5 or b = 2
Finding 'a' Correspondingly
1. If b = 2:
- a = 2 + 3 = 5
2. If b = -5:
- a = -5 + 3 = -2
Calculating 'ab'
Now, we calculate the product 'ab':
1. For a = 5 and b = 2:
- ab = 5 * 2 = 10
2. For a = -2 and b = -5:
- ab = -2 * -5 = 10
Conclusion
In both cases, the value of ab is:
- 10
Thus, the final answer is A. 10.
We have two key equations:
- a - b = 3 (Equation 1)
- a² + b² = 29 (Equation 2)
Finding 'a' and 'b'
From Equation 1, we can express 'a' in terms of 'b':
- a = b + 3
Now, substitute this expression for 'a' into Equation 2:
- (b + 3)² + b² = 29
Expanding the Equation
- (b² + 6b + 9) + b² = 29
- 2b² + 6b + 9 = 29
Simplifying the Equation
- 2b² + 6b + 9 - 29 = 0
- 2b² + 6b - 20 = 0
Dividing by 2
- b² + 3b - 10 = 0
Factoring the Quadratic
- (b + 5)(b - 2) = 0
Hence, the solutions are:
- b = -5 or b = 2
Finding 'a' Correspondingly
1. If b = 2:
- a = 2 + 3 = 5
2. If b = -5:
- a = -5 + 3 = -2
Calculating 'ab'
Now, we calculate the product 'ab':
1. For a = 5 and b = 2:
- ab = 5 * 2 = 10
2. For a = -2 and b = -5:
- ab = -2 * -5 = 10
Conclusion
In both cases, the value of ab is:
- 10
Thus, the final answer is A. 10.
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Ques4. If a - b = 3 and a2 + b2 = 29, find the value of ab.A. 10B. 12C. 15D. 18?
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Ques4. If a - b = 3 and a2 + b2 = 29, find the value of ab.A. 10B. 12C. 15D. 18? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Ques4. If a - b = 3 and a2 + b2 = 29, find the value of ab.A. 10B. 12C. 15D. 18? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Ques4. If a - b = 3 and a2 + b2 = 29, find the value of ab.A. 10B. 12C. 15D. 18?.
Ques4. If a - b = 3 and a2 + b2 = 29, find the value of ab.A. 10B. 12C. 15D. 18? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Ques4. If a - b = 3 and a2 + b2 = 29, find the value of ab.A. 10B. 12C. 15D. 18? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Ques4. If a - b = 3 and a2 + b2 = 29, find the value of ab.A. 10B. 12C. 15D. 18?.
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