If x=2+√3 find the value of (X+1/x)^3
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Answer:
(x + 1/x)³ = 64
Solution:
- Given : x = 2 + √3
- To find : (x + 1/x)³ = ?
We have ;
x = 2 + √3
Thus,
=> 1/x = 1/(2 + √3)
=> 1/x = (2 - √3)/(2 + √3)(2 - √3)
=> 1/x = (2 - √3)/[2² - (√3)²]
=> 1/x = (2 - √3)/(4 - 3)
=> 1/x = (2 - √3)/1
=> 1/x = 2 - √3
Now,
=> x + 1/x = (2 + √3) + (2 - √3)
=> x + 1/x = 2 + √3 + 2 - √3
=> x + 1/x = 4
Now,
Cubing both the sides , we get ;
=> (x + 1/x)³ = 4³
=> (x + 1/x)³ = 64
Hence,
Required answer is 64 .
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