Math, asked by anuhm3403, 6 hours ago

if x=2+√3 then x+1 by x is​

Answers

Answered by Anonymous
6

Step-by-step explanation:

if \:  \: x=2+ \sqrt{3}

Find :-

x +  \frac{1}{x}

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

On rationalise the denominator :-

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

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

 \frac{1}{x}  =  \frac{2 -  \sqrt{3} }{( {2}^{2} ) - ( { \sqrt{3}) }^{2} }

 \frac{1}{x}  =  \frac{2 -  \sqrt{3} }{4 - 3}

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

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

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

 = 4

I hope it is helpful

Answered by sandy1816
0

given

x= 2 + √3

so we can write

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

rationalizing the denominator we get

 \frac{1}{x}  =  \frac{1}{2 +  \sqrt{3} }  \times  \frac{2 -  \sqrt{3} }{2 -  \sqrt{3} }  \\  \\  \frac{1}{x}  =  \frac{2 -  \sqrt{3} }{4 - 3}  \\  \\  \frac{1}{x}  = 2 -  \sqrt{3}

Now

x +  \frac{1}{x}  = 2 -  \sqrt{3}  + 2 +  \sqrt{3}  \\  \\ x +  \frac{1}{x}  = 4

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