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If x=9+4 root 5 find the value of root x - 1/root x?
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If x=9+4 root 5 find the value of root x - 1/root x?
Given:
x = 9 + 4√5
To find:
√x - 1/√x
Solution:
Step 1: Find the value of x
Given x = 9 + 4√5
Now, let's square both sides to find x:
x^2 = (9 + 4√5)^2
x^2 = 81 + 36 + 72√5
x^2 = 117 + 72√5
Therefore, x = √(117 + 72√5)
Step 2: Find √x - 1/√x
√x - 1/√x = √(117 + 72√5) - 1/√(117 + 72√5)
To rationalize the denominator, multiply by the conjugate:
√x - 1/√x = (√(117 + 72√5) - 1/√(117 + 72√5)) * (√(117 + 72√5) + 1/√(117 + 72√5))
√x - 1/√x = (117 + 72√5 - 1)/117 + 72√5
√x - 1/√x = (116 + 72√5)/117 + 72√5
Therefore, the value of √x - 1/√x is (116 + 72√5)/117 + 72√5.
x = 9 + 4√5
To find:
√x - 1/√x
Solution:
Step 1: Find the value of x
Given x = 9 + 4√5
Now, let's square both sides to find x:
x^2 = (9 + 4√5)^2
x^2 = 81 + 36 + 72√5
x^2 = 117 + 72√5
Therefore, x = √(117 + 72√5)
Step 2: Find √x - 1/√x
√x - 1/√x = √(117 + 72√5) - 1/√(117 + 72√5)
To rationalize the denominator, multiply by the conjugate:
√x - 1/√x = (√(117 + 72√5) - 1/√(117 + 72√5)) * (√(117 + 72√5) + 1/√(117 + 72√5))
√x - 1/√x = (117 + 72√5 - 1)/117 + 72√5
√x - 1/√x = (116 + 72√5)/117 + 72√5
Therefore, the value of √x - 1/√x is (116 + 72√5)/117 + 72√5.
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If x=9+4 root 5 find the value of root x - 1/root x?
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If x=9+4 root 5 find the value of root x - 1/root x? 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 x=9+4 root 5 find the value of root x - 1/root x? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x=9+4 root 5 find the value of root x - 1/root x?.
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