If a=2+√3, then (a+1/a)³=
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a=2+√3.
(a+1/a)³=?.
1/a=1/2+√3.
Rationalising denominator of 2+√3 is 2-√3.
Multiply numerator & denominator by 2-√3.
1/2+√3×2-√3/2-√3.
2-√3/(2)²-(√3)². (Because a+b×a-b=a²- b² where a=2 & b=√3).
2-√3/4-3.
2-√3/1.
1/a=1/2+√3=2-√3.
(a+1/a)³=(2+√3+2-√3)³.
=(4)³.
=64.
I think this is your answer.
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