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If x=2+sqrt(3) , find the value of x^3+1...

If `x=2+sqrt(3)` , find the value of `x^3+1/(x^3)`

Text Solution

Verified by Experts

Given,
`x=2+sqrt3`.
​ Now,
`1/x=1/ (2+sqrt3)`
​​`=(2-sqrt3)/(2^2-sqrt 3^2)`​
`=2-sqrt3`
Then, `x+1/x=4...(i)`
Now,`x^3+1/x^3`
`=(x+1/x)^3-3xx(x)xx(1/x)xx(x+1/x)`
`=4^3-3(4)`
`=64-12`
`=52`.
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