please solve questions no 7
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x = 2 + 2^(2/3) + 2^(1/3) (given)
x - 2 = 2^(2/3) + 2^(1/3)
(x-2)^3 = [2^(2/3)+2^(1/3)]^3 ( cubing on both sides)
x^3 - 8 - 6x(x-2) = 2^2 + 2^1 + 3*[2^{(2/3)+(1/3)}[2^(2/3)+2^(1/3)
((by using this formula on R.H.S
((a+b)^3= a^3+b^3+3ab(a+b)) & minus one in L.H.S ))
or x^3 - 8 - 6x^2 + 12x = 4 + 2 + 6(x-2)
or x^3 - 8 -6x^2 + 12x = 6 + 6x - 12
or x^3 - 6x^2 +6x = 2
x - 2 = 2^(2/3) + 2^(1/3)
(x-2)^3 = [2^(2/3)+2^(1/3)]^3 ( cubing on both sides)
x^3 - 8 - 6x(x-2) = 2^2 + 2^1 + 3*[2^{(2/3)+(1/3)}[2^(2/3)+2^(1/3)
((by using this formula on R.H.S
((a+b)^3= a^3+b^3+3ab(a+b)) & minus one in L.H.S ))
or x^3 - 8 - 6x^2 + 12x = 4 + 2 + 6(x-2)
or x^3 - 8 -6x^2 + 12x = 6 + 6x - 12
or x^3 - 6x^2 +6x = 2
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