Math, asked by sanikamadavi9, 7 months ago

if x=3+2√2, then find x+1/x?​

Answers

Answered by anindyaadhikari13
5

\bf\large\underline\blue{Question:-}

  • If x=3+2\sqrt{2}, find the value of x+\frac{1}{x}

\bf\large\underline\blue{Solution:-}

x  = 3 +  2\sqrt{2}

\bf\small\underline\blue{Therefore,}

 \frac{1}{x}  =  \frac{1}{3 + 2 \sqrt{2} }

Now, we have to rationalize the denominator.

Rationalizing means to remove all the surds from the denominator.

\bf\small\underline\blue{Therefore,}

 \frac{1}{3 + 2 \sqrt{2} }

 =  \frac{1}{(3 + 2 \sqrt{2} )}  \times  \frac{(3 - 2 \sqrt{2} )}{(3 -  2\sqrt{2} )}

 =  \frac{3 - 2 \sqrt{2} }{ {(3)}^{2}  -  {(2 \sqrt{2}) }^{2} }

 =  \frac{3 - 2 \sqrt{2} }{9 - 8}

 =  \frac{3 - 2 \sqrt{2} }{1}

 = 3 - 2 \sqrt{2}

\bf\small\underline\blue{Therefore}

x +  \frac{1}{x}  = 3 + 2 \sqrt{2}  + 3 - 2 \sqrt{2}

 = 3 + 3 +  \cancel{2 \sqrt{2} } -  \cancel{2 \sqrt{2} }

 = 6

\bf\small\underline\blue{Therefore,}

x +  \frac{1}{x}  = 6

\bf\large\underline\blue{Answer:-}

  • The value of x +  \frac{1}{x} is 6
Answered by nandhireddysharada27
0
  1. Step-by-step explanation:

i hope it helps u

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