TS ICET 2017 Question Paper with Solutions for online practice

Question : 81 of 200

Marks: +1, -0

x = 3 + 3 ^ { { 1 } /{ 3 } } + 3 ^ { { 2 } /{ 3 } }

⇒

x ^ { 3 } - 9 x ^ { 2 } + 18 x - 12 =

Solution:

Given :

x=3+3^{1/3}+3^{2/3}

⇒(x-3)=3^{23}+3^{13}⇒(x-3)^{3}=(3^{2/3}+3^{1/3})^{3}

⇒x^{3}-27+27x-9x^{2}=9+3+3×3^{2/3}×3^{1/3}(3^{2/3}+3^{1/3})

⇒x^{3}-27+27x-9x^{2}=12+9(x-3)

⇒x^{3}-9x^{2}+27x-27=12+9x-27

⇒x^{3}-9x^{2}+18x-12=0

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