Verified answer

G i v e n :

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[tex]:\implies\sf{x=2+\sqrt{3}}[/tex]

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[tex]:\implies\sf{\dfrac{1}{x}=\dfrac{1}{2+\sqrt{3}}}[/tex]

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[tex]:\implies\sf{\dfrac{1}{x}=\dfrac{1}{2+\sqrt{3}}\times\dfrac{2-\sqrt{3}}{2-\sqrt{3}}}[/tex]

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• (a + b) (a - b) = a² - b²

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[tex]:\implies\sf{\dfrac{1}{x}=\dfrac{2-\sqrt{3}}{(2)^2-(\sqrt{3})^2}}[/tex]

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[tex]:\implies\sf{\dfrac{1}{x}=\dfrac{2-\sqrt{3}}{4-3}}[/tex]

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[tex]:\implies\sf{\dfrac{1}{x}=2-\sqrt{3}}[/tex]

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S o l u t i o n :

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[tex]:\implies\sf{x^3+\dfrac{1}{x^3}}[/tex]

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[tex]:\implies\sf{(2+\sqrt{3})^3+(2-\sqrt{3})^3}[/tex]

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• (a + b)³ = a³ + 3a²b + 3ab² + b³
• (a - b)³ = a³ - 3a²b + 3ab² - b³

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[tex]:\implies\sf{(2)^3+3(2)^2(\sqrt{3})+3(2)(\sqrt{3})^2+(\sqrt{3})^3+(2)^3-3(2)^2(\sqrt{3})+3(2)(\sqrt{3})^2-(\sqrt{3})^3}[/tex]

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[tex]:\implies\sf{8+12\sqrt{3}+18+3\sqrt{3}+8-12\sqrt{3}+18-3\sqrt{3}}[/tex]

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[tex]:\implies\underline{\boxed{\frak{\textcolor{lavender}{x^3+\cfrac{1}{x^3}=52}}}}\;\bigstar[/tex]

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Answer:

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Step-by-step explanation:

GM!!

sorry yesterday I had slept