Question

In rationalisation what is the answer of the ques if a=2+sqrt3 find the value of a+(1/a)

Answer 1

Hi ,

a = 2 + √3

1/a = 1/ ( 2 + √3 )

= ( 2 - √3 )/ [ (2 + √3)(2 - √3 )]

= ( 2 - √3 )/[ 2² - ( √3 )² ]

= ( 2 - √3 ) / ( 4 - 3 )

= 2 - √3

Therefore ,

a + 1/a = 2 + √3 + 2 - √3

= 4

I hope this helps you.

:)

Answer 2

1/a=(2-√3)/(2²-√3²) 1/a=(2-√3)/(4-3) 1/a=(2-√3)/1=2-√3 Here a+1/a=2+√3 +2-√3 A+1/a=4 Aliter a+1/a=(a²+1)/a =[(2+√3)²+1]/(2+√3) =[4+3+4√3+1]/(2+√3) =(8+4√3)/(2+√3) =4(2+√3)/(2+√3) =4 Hence a+1/a=4.