#(sqrt(6)+sqrt(2))/(sqrt(6)-sqrt(2)) + (sqrt(6)-sqrt(2))/(sqrt(6)+sqrt(2))# ?

1 Answer
Steve M
Apr 9, 2018

# (sqrt(6)+sqrt(2))/(sqrt(6)-sqrt(2)) + (sqrt(6)-sqrt(2))/(sqrt(6)+sqrt(2)) = 4#

Explanation:

We seek the value of the expression:

# E = (sqrt(6)+sqrt(2))/(sqrt(6)-sqrt(2)) + (sqrt(6)-sqrt(2))/(sqrt(6)+sqrt(2)) #

We can add the fractions using a common denominator, thus:

# E = ( (sqrt(6)+sqrt(2))(sqrt(6)+sqrt(2)) +(sqrt(6)-sqrt(2))(sqrt(6)-sqrt(2))) / ((sqrt(6)-sqrt(2))(sqrt(6)+sqrt(2)) #

# \ \ = ( ( sqrt(6)sqrt(6) + 2sqrt(2)sqrt(6) + sqrt(2)sqrt(2) )(sqrt(6)sqrt(6)-2sqrt(2)sqrt(6)+sqrt(2)sqrt(2) )) / ( sqrt(6)sqrt(6) - sqrt(2)sqrt(2)) #

# \ \ = ( ( 6 + 2sqrt(12) + 2 )(6-2sqrt(12)+2 )) / ( 6 - 2) #

# \ \ = ( ( 8 + 2sqrt(12))(8-2sqrt(12) )) / ( 4 ) #

# \ \ = ( 8*8-2sqrt(12) * 2sqrt(12)) / ( 4 ) #

# \ \ = ( 64-4*12) / ( 4 ) #

# \ \ = ( 64-48) / ( 4 ) #

# \ \ = ( 16) / ( 4 ) #

# \ \ = 4 #

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