If-2-1-3-4-1-3-8-1-3-x-then-x-3-6x-2-6x-6-

Question Number 83941 by john santu last updated on 08/Mar/20

If \sqrt[3]{2} + \sqrt[3]{4} + \sqrt[3]{8} = x

then x^{3} - {6 x}^{2} + 6 x + 6 = ?

Answered by $@ty@m123 last updated on 08/Mar/20

^{3} \sqrt{2} +^{3} \sqrt{4} + 2 = x

^{3} \sqrt{2} +^{3} \sqrt{4} = x - 2

{(^{3} \sqrt{2} +^{3} \sqrt{4})}^{3} = {(x - 2)}^{3}

2 + 4 + 3 .^{3} \sqrt{8} (^{3} \sqrt{2} +^{3} \sqrt{4}) = {(x - 2)}^{3}

6 + 3 \times 2 (^{3} \sqrt{2} +^{3} \sqrt{4}) = {(x - 2)}^{3}

6 + 6 (x - 2) = {(x - 2)}^{3}

6 + 6 x - 12 = x^{3} - 8 - 6 x^{2} + 12 x

x^{3} - 6 x^{2} + 6 x + 6 = 8

Commented by john santu last updated on 08/Mar/20

good \dots