If x=2+√3 then find the the value of √x+1/√x
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Given that x=3+2√3 we need to find √x+1/√x. Therefore we have-
(√x+1/√x)^2= x+1/x +2 ...........using (a+b)^2=a^2+b^2+2ab
Substituting the value of x-
=(3+2√3)+1/(3+2√3)+2
Now, rationalize 1/x-
=(9+6√3-3+2√3+6)/3
=(12+8√3)/3
=4(3+2√3)/3
.
. . (√x+1/√x)=±(√(4(3+2√3)/3)
=±(2√(3+2√3)/3)
(√x+1/√x)^2= x+1/x +2 ...........using (a+b)^2=a^2+b^2+2ab
Substituting the value of x-
=(3+2√3)+1/(3+2√3)+2
Now, rationalize 1/x-
=(9+6√3-3+2√3+6)/3
=(12+8√3)/3
=4(3+2√3)/3
.
. . (√x+1/√x)=±(√(4(3+2√3)/3)
=±(2√(3+2√3)/3)
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