x=2+√3findx³+1\x³Rd book
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x = 2 + √3
1/x = 1/(2 + √3)
= (2-√3)/(2 + √3)(2 -√3)
=(2 -√3)/(2² -√3²)
=(2 -√3)
hence, x + 1/x = 2 +√3 + 2 -√3 = 4
x³ + 1/x³ = (x +1/x)³-3(x +1/x)
= (4)³ -3(4)
= 64 -12 = 52
hence, x³ +1/x³ = 52
1/x = 1/(2 + √3)
= (2-√3)/(2 + √3)(2 -√3)
=(2 -√3)/(2² -√3²)
=(2 -√3)
hence, x + 1/x = 2 +√3 + 2 -√3 = 4
x³ + 1/x³ = (x +1/x)³-3(x +1/x)
= (4)³ -3(4)
= 64 -12 = 52
hence, x³ +1/x³ = 52
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