Class 9 Exam > Class 9 Questions > If x=2-√3,find the value of (x+1/x)^3?
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If x=2-√3,find the value of (x+1/x)^3?
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If x=2-√3,find the value of (x+1/x)^3?
Given:
x = 2 - √3
To find:
Value of (x + 1/x)^3
Solution:
Step 1: Find the value of 1/x
Since x = 2 - √3, we can find 1/x by taking the reciprocal of x:
1/x = 1/(2 - √3)
To rationalize the denominator, multiply the numerator and denominator by the conjugate of the denominator:
1/x = (2 + √3)/(2 - √3)(2 + √3)
1/x = (2 + √3)/(4 - 3)
1/x = 2 + √3
Step 2: Find the value of (x + 1/x)
Now, add x and 1/x:
x + 1/x = (2 - √3) + (2 + √3)
x + 1/x = 4
Step 3: Find the cube of (x + 1/x)
Now, cube the value of (x + 1/x):
(x + 1/x)^3 = 4^3
(x + 1/x)^3 = 64
Therefore, the value of (x + 1/x)^3 is 64.
x = 2 - √3
To find:
Value of (x + 1/x)^3
Solution:
Step 1: Find the value of 1/x
Since x = 2 - √3, we can find 1/x by taking the reciprocal of x:
1/x = 1/(2 - √3)
To rationalize the denominator, multiply the numerator and denominator by the conjugate of the denominator:
1/x = (2 + √3)/(2 - √3)(2 + √3)
1/x = (2 + √3)/(4 - 3)
1/x = 2 + √3
Step 2: Find the value of (x + 1/x)
Now, add x and 1/x:
x + 1/x = (2 - √3) + (2 + √3)
x + 1/x = 4
Step 3: Find the cube of (x + 1/x)
Now, cube the value of (x + 1/x):
(x + 1/x)^3 = 4^3
(x + 1/x)^3 = 64
Therefore, the value of (x + 1/x)^3 is 64.
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If x=2-√3,find the value of (x+1/x)^3?
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If x=2-√3,find the value of (x+1/x)^3? 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=2-√3,find the value of (x+1/x)^3? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x=2-√3,find the value of (x+1/x)^3?.
If x=2-√3,find the value of (x+1/x)^3? 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=2-√3,find the value of (x+1/x)^3? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x=2-√3,find the value of (x+1/x)^3?.
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