Question

if x=2+√3 find the value of x+1/x

Answer 1

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Given : x = ( 2 + √3 )            --------------- equation 1

So, 1 / x = 1 / ( 2 + √3 )   

To rationalize it , multiply its numerator and denominator  by ( 2 - √3 )

1 / x = 1 * ( 2 - √3 ) / ( 2 + √3 ) ( 2 - √3 )

By using identity ( a + b ) ( a - b ) = a² - b².

1 / x = ( 2 - √3 ) / { ( 2 )² - ( √3 )² }

1 / x = ( 2 - √3 ) / { 4 - 3 }

1 / x = ( 2 - √3 ) / 1

1 / x = ( 2 - √3 )                                    ----------------- equation 2.


By adding equation 1 and equation 2 ,

x + 1 / x = 2 + √3 + 2  - √3

x + 1 / x = 4.

Answer for this question is 4.


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Answer 2

X=2+root3
1÷x=1÷2+root3
Rationaliging=
1÷2+root3×2-root 3×2-root 3= 2-root3
Putting value=2+root3+2-root3=4
Answer=4