Math, asked by premshar06, 6 months ago

If x=2+√3 find (x+1/x)^3

Answers

Answered by TheWonderWall
4

\large\sf\underline{Given}

  • \sf\:x=2+\sqrt{3}

\large\sf\underline{To\:find}

  • \sf\:(x+\frac{1}{x})^{3}

\large\sf\underline{Solution}

As x = \sf\:2+\sqrt{3}

So \sf\:\frac{1}{x}=2-\sqrt{3}

Therefore :

\sf\:(x+\frac{1}{x})

\sf➙\:2+\sqrt{3}+2-\sqrt{3}

\sf➙\:2+2+\sqrt{3}-\sqrt{3}

{\sf{{\pink{➙\:4}}}}

Now substituting the value of \sf\:(x+\frac{1}{x}) in \sf\:(x+\frac{1}{x})^{3}

We get :

\sf\:(x+\frac{1}{x})^{3}

\sf➙\:4^{3}

{\sf{{\pink{➙\:64}}}}

  • Thnku :)
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