if x=2^2/3 + 2^1/3,then prove that x^3-6x-6=0
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x=2^(2/3)+2^(1/3)..(i)
Cubing both sides we get ,
=>x^3=2^(2/3×3)+2^(1/3×3)+
3.2^(2/3).2^(1/3)[2^(2/3)+2^(1/3)]
=>x^3=4+2+3.2^(2/3+1/3).(x)...fromeq i.
=>x^3=6+3.2(x)
=>x^3-6x-6=0.
Hope it helps
Cubing both sides we get ,
=>x^3=2^(2/3×3)+2^(1/3×3)+
3.2^(2/3).2^(1/3)[2^(2/3)+2^(1/3)]
=>x^3=4+2+3.2^(2/3+1/3).(x)...fromeq i.
=>x^3=6+3.2(x)
=>x^3-6x-6=0.
Hope it helps
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