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Question Number 194846 by dimentri last updated on 17/Jul/23

$$\underbrace{}$$

Answered by som(math1967) last updated on 17/Jul/23

$$x=\frac{\sqrt[3]{10+6\sqrt{3}}(\sqrt{3}-1)}{\sqrt{5+1+2\sqrt{5}}-\sqrt{5}}$$$$x=\frac{\sqrt[3]{3\sqrt{3}+3.3+3\sqrt{3}+1}(\sqrt{3}-1)}{\sqrt{{(\sqrt{5}+1)}^2}-\sqrt{5}}$$$$x=\frac{\sqrt[3]{{\left(\sqrt{3}\right)}^3+3.{\left(\sqrt{3}\right)}^2.1+3.\sqrt{3}.1+1^3}(\sqrt{3}-1)}{\sqrt{5}+1-\sqrt{5}}$$$$x=\frac{\sqrt[3]{{(\sqrt{3}+1)}^3}(\sqrt{3}-1)}{1}$$$$x=(\sqrt{3}+1)(\sqrt{3}-1)=2$$$$\therefore G={(12\times 2^3+4\times 2^2-55)}^{2023}$$$$={(96+16-55)}^{2023}$$$$={\left(57\right)}^{2023}$$

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