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Question
If `x=2^(1/3)+2^(2/3),` Show that x3 - 6x = 6
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Solution
x3 - 6x = 6
`x=2^(1/3)+2^(2/3)`
Putting cube on both the sides, we get,
`x^3=(2^(1/3)+2^(2/3))^3`
As we know, `(a+b)^3=a^3+b^3+3ab(a+b)`
`x^3=(2^(1/3))^3+(2^(2/3))^3+3(2^(1/3))(2^(2/3))(2^(1/3)+2^(2/3))`
`x^3=(2^(1/3))^3+(2^(2/3))^3+3(2^(1/3+2/3))(x)`
`x^3=(2^(3/3))+(2^(6/3))+3(2)(x)`
`x^3=2^1+2^2+3(2)(x)`
`x^3=2+4+6x`
`x^3=6+6x`
`x^3-6x=6`
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