X=2+√3
Find (x-1/x)^3
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given ,x= (2+√3)
(x-1/x)³=?
{(x/x)-(1/x)}³={1-1/x}³={1-(2+√3)}³={1-2+√3}³={1-√3}³
now we use (a-b)³=a³-b³+3ab²-3a²b
we have to find first ,1/x= 1/(2+√3)=(2-√3)
(1-√3)³=1-3√3+9-3√3
= 10-6√3
(x-1/x)³=?
{(x/x)-(1/x)}³={1-1/x}³={1-(2+√3)}³={1-2+√3}³={1-√3}³
now we use (a-b)³=a³-b³+3ab²-3a²b
we have to find first ,1/x= 1/(2+√3)=(2-√3)
(1-√3)³=1-3√3+9-3√3
= 10-6√3
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