Class 9 Exam > Class 9 Questions > If a=9-4root 5,then find the value of a-1/a?
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If a=9-4root 5,then find the value of a-1/a?
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If a=9-4root 5,then find the value of a-1/a?
A=9-4√5 1/a=1/9-4√5. ( rationalise) 1/a=9 4√5 a-1/a=9-4√5-(9 4√5) a-1/a=9-4√5-9-4√5 a-1/a= -8√5
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If a=9-4root 5,then find the value of a-1/a?
Solution:
To find the value of a - 1/a, we need to substitute the given value of a and simplify the expression.
Given: a = 9 - 4√5
To find a - 1/a, we will follow the following steps:
Step 1: Calculate the value of a:
Given a = 9 - 4√5
Step 2: Calculate the value of 1/a:
To find the reciprocal of a, we can calculate 1/a as follows:
1/a = 1 / (9 - 4√5)
Multiply both the numerator and denominator by the conjugate of the denominator, which is (9 + 4√5):
1/a = (1 / (9 - 4√5)) * ((9 + 4√5) / (9 + 4√5))
Simplify the expression:
1/a = (9 + 4√5) / (81 - 80)
1/a = (9 + 4√5) / 1
So, 1/a = 9 + 4√5
Step 3: Substitute the values of a and 1/a into the expression a - 1/a:
a - 1/a = (9 - 4√5) - (9 + 4√5)
Simplify the expression:
a - 1/a = 9 - 4√5 - 9 - 4√5
Combine like terms:
a - 1/a = -8√5
Therefore, the value of a - 1/a is -8√5.
To find the value of a - 1/a, we need to substitute the given value of a and simplify the expression.
Given: a = 9 - 4√5
To find a - 1/a, we will follow the following steps:
Step 1: Calculate the value of a:
Given a = 9 - 4√5
Step 2: Calculate the value of 1/a:
To find the reciprocal of a, we can calculate 1/a as follows:
1/a = 1 / (9 - 4√5)
Multiply both the numerator and denominator by the conjugate of the denominator, which is (9 + 4√5):
1/a = (1 / (9 - 4√5)) * ((9 + 4√5) / (9 + 4√5))
Simplify the expression:
1/a = (9 + 4√5) / (81 - 80)
1/a = (9 + 4√5) / 1
So, 1/a = 9 + 4√5
Step 3: Substitute the values of a and 1/a into the expression a - 1/a:
a - 1/a = (9 - 4√5) - (9 + 4√5)
Simplify the expression:
a - 1/a = 9 - 4√5 - 9 - 4√5
Combine like terms:
a - 1/a = -8√5
Therefore, the value of a - 1/a is -8√5.
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If a=9-4root 5,then find the value of a-1/a?
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If a=9-4root 5,then find the value of a-1/a? 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=9-4root 5,then find the value of a-1/a? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a=9-4root 5,then find the value of a-1/a?.
If a=9-4root 5,then find the value of a-1/a? 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=9-4root 5,then find the value of a-1/a? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a=9-4root 5,then find the value of a-1/a?.
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