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Find the value of a if 3 minus under root 5 upon 3 2 under root 5 is equal to a under root 5inus 19 upon 11?
Most Upvoted Answer
Find the value of a if 3 minus under root 5 upon 3 2 under root 5 is...
Solution:
Given: 3 - sqrt(5)/3 * 2sqrt(5) = a * sqrt(5) - 19/11
To Find: Value of a
Step 1: Simplify the left-hand side of the equation
We know that 3 - sqrt(5) = (3sqrt(5) - sqrt(5)^2)/3 = (3sqrt(5) - 5)/3
Therefore, 3 - sqrt(5)/3 * 2sqrt(5) = (3sqrt(5) - 5)/3 * 2sqrt(5)/3 = (6sqrt(5) - 10)/9
So, our equation becomes:
(6sqrt(5) - 10)/9 = a * sqrt(5) - 19/11
Step 2: Multiply both sides by 99 to eliminate the denominators
99 * (6sqrt(5) - 10)/9 = 99 * (a * sqrt(5) - 19/11)
Simplifying this equation, we get:
22(6sqrt(5) - 10) = 9a * sqrt(5) * 99 - 19 * 99
Step 3: Solve for a
Expanding the left-hand side of the equation, we get:
132sqrt(5) - 220 = 891a * sqrt(5) - 1881
Grouping the terms with sqrt(5), we get:
(132 - 891a) * sqrt(5) = 1699
Dividing both sides by sqrt(5), we get:
132 - 891a = 1699/sqrt(5)
Solving for a, we get:
a = (132 - 1699/sqrt(5))/891
Simplifying, we get:
a = (132sqrt(5) - 1699)/4455
Therefore, the value of a is (132sqrt(5) - 1699)/4455.
Given: 3 - sqrt(5)/3 * 2sqrt(5) = a * sqrt(5) - 19/11
To Find: Value of a
Step 1: Simplify the left-hand side of the equation
We know that 3 - sqrt(5) = (3sqrt(5) - sqrt(5)^2)/3 = (3sqrt(5) - 5)/3
Therefore, 3 - sqrt(5)/3 * 2sqrt(5) = (3sqrt(5) - 5)/3 * 2sqrt(5)/3 = (6sqrt(5) - 10)/9
So, our equation becomes:
(6sqrt(5) - 10)/9 = a * sqrt(5) - 19/11
Step 2: Multiply both sides by 99 to eliminate the denominators
99 * (6sqrt(5) - 10)/9 = 99 * (a * sqrt(5) - 19/11)
Simplifying this equation, we get:
22(6sqrt(5) - 10) = 9a * sqrt(5) * 99 - 19 * 99
Step 3: Solve for a
Expanding the left-hand side of the equation, we get:
132sqrt(5) - 220 = 891a * sqrt(5) - 1881
Grouping the terms with sqrt(5), we get:
(132 - 891a) * sqrt(5) = 1699
Dividing both sides by sqrt(5), we get:
132 - 891a = 1699/sqrt(5)
Solving for a, we get:
a = (132 - 1699/sqrt(5))/891
Simplifying, we get:
a = (132sqrt(5) - 1699)/4455
Therefore, the value of a is (132sqrt(5) - 1699)/4455.
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Find the value of a if 3 minus under root 5 upon 3 2 under root 5 is...
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Find the value of a if 3 minus under root 5 upon 3 2 under root 5 is equal to a under root 5inus 19 upon 11?
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Find the value of a if 3 minus under root 5 upon 3 2 under root 5 is equal to a under root 5inus 19 upon 11? 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 Find the value of a if 3 minus under root 5 upon 3 2 under root 5 is equal to a under root 5inus 19 upon 11? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the value of a if 3 minus under root 5 upon 3 2 under root 5 is equal to a under root 5inus 19 upon 11?.
Find the value of a if 3 minus under root 5 upon 3 2 under root 5 is equal to a under root 5inus 19 upon 11? 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 Find the value of a if 3 minus under root 5 upon 3 2 under root 5 is equal to a under root 5inus 19 upon 11? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the value of a if 3 minus under root 5 upon 3 2 under root 5 is equal to a under root 5inus 19 upon 11?.
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