If a=2+√3,find a+1/a
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Hey Mate!
Since, a=2+root 3
then 1/a=1/2+root 3
[we have to change irrational number in denominator to a rational number]
SO,
1/2+√3*2-√3/2-√3
[here signs will change it will be 2-√3 and we have to multiply this number in numerator as well as denominator]
Answer after multiplying will be:
2-√3/ (2)^2 -(√3)^2 [using identity (a+b) (a-b)=a^2 - b^2]
2-√3/4-3=2-√3/1
therefore, 1/a= 2-√3
NOW,
a+1/a = 2+√3+2-√3
so here, √3 will cut {because + and- signs are cut}
and left over numbers will be 2+2
Therefore, Solution is 4
We will find 1/a because value of a is known and then question will be solved.....
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