Class 9 Exam > Class 9 Questions > If a =sqrt 3-sqrt 2/sqrt 3+sqrt 2 and b=sqrt ...
Start Learning for Free
If a =sqrt 3-sqrt 2/sqrt 3+sqrt 2 and b=sqrt 3+sqrt 2/sqrt 3-sqrt 2, find the value of a^2+b^2-5ab?
Most Upvoted Answer
If a =sqrt 3-sqrt 2/sqrt 3+sqrt 2 and b=sqrt 3+sqrt 2/sqrt 3-sqrt 2, f...
Calculating a and b values:
We need to calculate the values of a and b before proceeding with the main calculation.
a = (sqrt(3) - sqrt(2)) / (sqrt(3) * sqrt(2))
b = (sqrt(3) * sqrt(2)) / (sqrt(3) - sqrt(2))
Simplifying the above expressions will give us:
a = sqrt(3)/sqrt(2) - 1
b = sqrt(3)/sqrt(2) + 1
Calculating a^2 b^2:
a^2 b^2 can be calculated by simply squaring a and b and then multiplying them.
a^2 = (sqrt(3)/sqrt(2) - 1)^2 = 3/2 - 2sqrt(3)/2 + 1 = 5/2 - sqrt(3)
b^2 = (sqrt(3)/sqrt(2) + 1)^2 = 3/2 + 2sqrt(3)/2 + 1 = 5/2 + sqrt(3)
a^2 b^2 = (5/2 - sqrt(3)) * (5/2 + sqrt(3)) = 25/4 - 3
a^2 b^2 = 19/4
Calculating 5ab:
5ab can be calculated by multiplying 5 with the product of a and b.
5ab = 5 * (sqrt(3)/sqrt(2) - 1) * (sqrt(3)/sqrt(2) + 1)
5ab = 5 * ((3/2) - 1)
5ab = 5/2
Final Calculation:
Substituting the values of a^2 b^2 and 5ab in the given expression:
a^2 b^2 - 5ab = 19/4 - 5/2
a^2 b^2 - 5ab = -1/4
Therefore, the value of a^2 b^2 - 5ab is -1/4.
We need to calculate the values of a and b before proceeding with the main calculation.
a = (sqrt(3) - sqrt(2)) / (sqrt(3) * sqrt(2))
b = (sqrt(3) * sqrt(2)) / (sqrt(3) - sqrt(2))
Simplifying the above expressions will give us:
a = sqrt(3)/sqrt(2) - 1
b = sqrt(3)/sqrt(2) + 1
Calculating a^2 b^2:
a^2 b^2 can be calculated by simply squaring a and b and then multiplying them.
a^2 = (sqrt(3)/sqrt(2) - 1)^2 = 3/2 - 2sqrt(3)/2 + 1 = 5/2 - sqrt(3)
b^2 = (sqrt(3)/sqrt(2) + 1)^2 = 3/2 + 2sqrt(3)/2 + 1 = 5/2 + sqrt(3)
a^2 b^2 = (5/2 - sqrt(3)) * (5/2 + sqrt(3)) = 25/4 - 3
a^2 b^2 = 19/4
Calculating 5ab:
5ab can be calculated by multiplying 5 with the product of a and b.
5ab = 5 * (sqrt(3)/sqrt(2) - 1) * (sqrt(3)/sqrt(2) + 1)
5ab = 5 * ((3/2) - 1)
5ab = 5/2
Final Calculation:
Substituting the values of a^2 b^2 and 5ab in the given expression:
a^2 b^2 - 5ab = 19/4 - 5/2
a^2 b^2 - 5ab = -1/4
Therefore, the value of a^2 b^2 - 5ab is -1/4.
Community Answer
If a =sqrt 3-sqrt 2/sqrt 3+sqrt 2 and b=sqrt 3+sqrt 2/sqrt 3-sqrt 2, f...
Attention Class 9 Students!
To make sure you are not studying endlessly, EduRev has designed Class 9 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 9.
|
Explore Courses for Class 9 exam
|
|
Similar Class 9 Doubts
Top Courses for Class 9View all
If a =sqrt 3-sqrt 2/sqrt 3+sqrt 2 and b=sqrt 3+sqrt 2/sqrt 3-sqrt 2, find the value of a^2+b^2-5ab?
Question Description
If a =sqrt 3-sqrt 2/sqrt 3+sqrt 2 and b=sqrt 3+sqrt 2/sqrt 3-sqrt 2, find the value of a^2+b^2-5ab? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about If a =sqrt 3-sqrt 2/sqrt 3+sqrt 2 and b=sqrt 3+sqrt 2/sqrt 3-sqrt 2, find the value of a^2+b^2-5ab? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a =sqrt 3-sqrt 2/sqrt 3+sqrt 2 and b=sqrt 3+sqrt 2/sqrt 3-sqrt 2, find the value of a^2+b^2-5ab?.
If a =sqrt 3-sqrt 2/sqrt 3+sqrt 2 and b=sqrt 3+sqrt 2/sqrt 3-sqrt 2, find the value of a^2+b^2-5ab? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about If a =sqrt 3-sqrt 2/sqrt 3+sqrt 2 and b=sqrt 3+sqrt 2/sqrt 3-sqrt 2, find the value of a^2+b^2-5ab? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a =sqrt 3-sqrt 2/sqrt 3+sqrt 2 and b=sqrt 3+sqrt 2/sqrt 3-sqrt 2, find the value of a^2+b^2-5ab?.
Solutions for If a =sqrt 3-sqrt 2/sqrt 3+sqrt 2 and b=sqrt 3+sqrt 2/sqrt 3-sqrt 2, find the value of a^2+b^2-5ab? in English & in Hindi are available as part of our courses for Class 9.
Download more important topics, notes, lectures and mock test series for Class 9 Exam by signing up for free.
Here you can find the meaning of If a =sqrt 3-sqrt 2/sqrt 3+sqrt 2 and b=sqrt 3+sqrt 2/sqrt 3-sqrt 2, find the value of a^2+b^2-5ab? defined & explained in the simplest way possible. Besides giving the explanation of
If a =sqrt 3-sqrt 2/sqrt 3+sqrt 2 and b=sqrt 3+sqrt 2/sqrt 3-sqrt 2, find the value of a^2+b^2-5ab?, a detailed solution for If a =sqrt 3-sqrt 2/sqrt 3+sqrt 2 and b=sqrt 3+sqrt 2/sqrt 3-sqrt 2, find the value of a^2+b^2-5ab? has been provided alongside types of If a =sqrt 3-sqrt 2/sqrt 3+sqrt 2 and b=sqrt 3+sqrt 2/sqrt 3-sqrt 2, find the value of a^2+b^2-5ab? theory, EduRev gives you an
ample number of questions to practice If a =sqrt 3-sqrt 2/sqrt 3+sqrt 2 and b=sqrt 3+sqrt 2/sqrt 3-sqrt 2, find the value of a^2+b^2-5ab? tests, examples and also practice Class 9 tests.
|
|
Explore Courses for Class 9 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
|
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