UPSC Exam > UPSC Questions > For the identity (7+root5)/(7-root5) - (7-roo...
Start Learning for Free
For the identity (7+root5)/(7-root5) - (7-root5)/(7+root5) = a+7root5b
identify a,b?
identify a,b?
Most Upvoted Answer
For the identity (7+root5)/(7-root5) - (7-root5)/(7+root5) = a+7root5b...
Step 1: Simplifying the Expression
To solve the identity
(7 + √5)/(7 - √5) - (7 - √5)/(7 + √5),
we need to simplify each term.
Step 2: Finding a Common Denominator
- The common denominator of the two fractions is (7 - √5)(7 + √5).
Step 3: Combining the Fractions
- Rewrite the equation:
[(7 + √5)(7 + √5) - (7 - √5)(7 - √5)] / [(7 - √5)(7 + √5)]
Step 4: Expanding the Numerator
- Expand both products in the numerator:
(7 + √5)² = 49 + 14√5 + 5 = 54 + 14√5
(7 - √5)² = 49 - 14√5 + 5 = 54 - 14√5
- Subtract the second from the first:
(54 + 14√5) - (54 - 14√5) = 28√5
Step 5: Simplifying the Denominator
- The denominator simplifies to:
(7 - √5)(7 + √5) = 49 - 5 = 44
Step 6: Final Expression
- The expression now looks like:
28√5 / 44 = (7/11)√5
Step 7: Identifying a and b
- Comparing with a + 7√5b:
a = 0, b = 1/11
Conclusion
Thus, we find:
- a = 0
- b = 1/11
This completes the identification of a and b in the given expression.
To solve the identity
(7 + √5)/(7 - √5) - (7 - √5)/(7 + √5),
we need to simplify each term.
Step 2: Finding a Common Denominator
- The common denominator of the two fractions is (7 - √5)(7 + √5).
Step 3: Combining the Fractions
- Rewrite the equation:
[(7 + √5)(7 + √5) - (7 - √5)(7 - √5)] / [(7 - √5)(7 + √5)]
Step 4: Expanding the Numerator
- Expand both products in the numerator:
(7 + √5)² = 49 + 14√5 + 5 = 54 + 14√5
(7 - √5)² = 49 - 14√5 + 5 = 54 - 14√5
- Subtract the second from the first:
(54 + 14√5) - (54 - 14√5) = 28√5
Step 5: Simplifying the Denominator
- The denominator simplifies to:
(7 - √5)(7 + √5) = 49 - 5 = 44
Step 6: Final Expression
- The expression now looks like:
28√5 / 44 = (7/11)√5
Step 7: Identifying a and b
- Comparing with a + 7√5b:
a = 0, b = 1/11
Conclusion
Thus, we find:
- a = 0
- b = 1/11
This completes the identification of a and b in the given expression.
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
For the identity (7+root5)/(7-root5) - (7-root5)/(7+root5) = a+7root5bidentify a,b?
Question Description
For the identity (7+root5)/(7-root5) - (7-root5)/(7+root5) = a+7root5bidentify a,b? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about For the identity (7+root5)/(7-root5) - (7-root5)/(7+root5) = a+7root5bidentify a,b? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For the identity (7+root5)/(7-root5) - (7-root5)/(7+root5) = a+7root5bidentify a,b?.
For the identity (7+root5)/(7-root5) - (7-root5)/(7+root5) = a+7root5bidentify a,b? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about For the identity (7+root5)/(7-root5) - (7-root5)/(7+root5) = a+7root5bidentify a,b? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For the identity (7+root5)/(7-root5) - (7-root5)/(7+root5) = a+7root5bidentify a,b?.
Solutions for For the identity (7+root5)/(7-root5) - (7-root5)/(7+root5) = a+7root5bidentify a,b? 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 For the identity (7+root5)/(7-root5) - (7-root5)/(7+root5) = a+7root5bidentify a,b? defined & explained in the simplest way possible. Besides giving the explanation of
For the identity (7+root5)/(7-root5) - (7-root5)/(7+root5) = a+7root5bidentify a,b?, a detailed solution for For the identity (7+root5)/(7-root5) - (7-root5)/(7+root5) = a+7root5bidentify a,b? has been provided alongside types of For the identity (7+root5)/(7-root5) - (7-root5)/(7+root5) = a+7root5bidentify a,b? theory, EduRev gives you an
ample number of questions to practice For the identity (7+root5)/(7-root5) - (7-root5)/(7+root5) = a+7root5bidentify a,b? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup