UPSC Exam > UPSC Questions > If a - b = 3 and a2 + b2 = 29, find the value...
Start Learning for Free
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
If a - b = 3 and a2 + b2 = 29, find the value of ab.A. 10B. 12C. 15D. ...
Given Equations
To solve the equations, we have:
- a - b = 3 (Equation 1)
- a² + b² = 29 (Equation 2)
Step 1: Express 'a' in terms of 'b'
From Equation 1, we can express 'a' as:
- a = b + 3
Step 2: Substitute 'a' in Equation 2
Now, we substitute 'a' in Equation 2:
- (b + 3)² + b² = 29
Expanding the equation:
- (b² + 6b + 9) + b² = 29
- 2b² + 6b + 9 = 29
Step 3: Simplify the equation
Rearranging this gives us:
- 2b² + 6b + 9 - 29 = 0
- 2b² + 6b - 20 = 0
Now, simplifying further:
- b² + 3b - 10 = 0
Step 4: Factor the quadratic equation
We can factor this as:
- (b + 5)(b - 2) = 0
So, the solutions for 'b' are:
- b = -5 or b = 2
Step 5: Find corresponding 'a' values
Using these 'b' values to find 'a':
- If b = 2: a = 2 + 3 = 5
- If b = -5: a = -5 + 3 = -2
Now, we have two pairs: (5, 2) and (-2, -5).
Step 6: Calculate 'ab'
Now, calculating 'ab' for both pairs:
- For (5, 2): ab = 5 * 2 = 10
- For (-2, -5): ab = -2 * -5 = 10
Final Answer
The value of ab is 10.
Thus, the correct answer is A. 10.
To solve the equations, we have:
- a - b = 3 (Equation 1)
- a² + b² = 29 (Equation 2)
Step 1: Express 'a' in terms of 'b'
From Equation 1, we can express 'a' as:
- a = b + 3
Step 2: Substitute 'a' in Equation 2
Now, we substitute 'a' in Equation 2:
- (b + 3)² + b² = 29
Expanding the equation:
- (b² + 6b + 9) + b² = 29
- 2b² + 6b + 9 = 29
Step 3: Simplify the equation
Rearranging this gives us:
- 2b² + 6b + 9 - 29 = 0
- 2b² + 6b - 20 = 0
Now, simplifying further:
- b² + 3b - 10 = 0
Step 4: Factor the quadratic equation
We can factor this as:
- (b + 5)(b - 2) = 0
So, the solutions for 'b' are:
- b = -5 or b = 2
Step 5: Find corresponding 'a' values
Using these 'b' values to find 'a':
- If b = 2: a = 2 + 3 = 5
- If b = -5: a = -5 + 3 = -2
Now, we have two pairs: (5, 2) and (-2, -5).
Step 6: Calculate 'ab'
Now, calculating 'ab' for both pairs:
- For (5, 2): ab = 5 * 2 = 10
- For (-2, -5): ab = -2 * -5 = 10
Final Answer
The value of ab is 10.
Thus, the correct answer is A. 10.
Attention UPSC Students!
To make sure you are not studying endlessly, EduRev has designed UPSC study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in UPSC.
|
Explore Courses for UPSC exam
|
|
Top Courses for UPSCView all
If a - b = 3 and a2 + b2 = 29, find the value of ab.A. 10B. 12C. 15D. 18?
Question Description
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 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 If a - b = 3 and a2 + b2 = 29, find the value of ab.A. 10B. 12C. 15D. 18?.
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 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 If a - b = 3 and a2 + b2 = 29, find the value of ab.A. 10B. 12C. 15D. 18?.
Solutions for If a - b = 3 and a2 + b2 = 29, find the value of ab.A. 10B. 12C. 15D. 18? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of If a - b = 3 and a2 + b2 = 29, find the value of ab.A. 10B. 12C. 15D. 18? defined & explained in the simplest way possible. Besides giving the explanation of
If a - b = 3 and a2 + b2 = 29, find the value of ab.A. 10B. 12C. 15D. 18?, a detailed solution for If a - b = 3 and a2 + b2 = 29, find the value of ab.A. 10B. 12C. 15D. 18? has been provided alongside types of If a - b = 3 and a2 + b2 = 29, find the value of ab.A. 10B. 12C. 15D. 18? theory, EduRev gives you an
ample number of questions to practice If a - b = 3 and a2 + b2 = 29, find the value of ab.A. 10B. 12C. 15D. 18? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup