Posted by **Bob** on Monday, May 6, 2013 at 1:45am.

If the sum of 3 non-zero distinct real numbers a, b, and c is 2, and the two sets {a,b,c} and {1/a,1/b,1/c} are the same, what is the value of a^2+b^2+c^2?

Note: Two sets are the same if there is a one-to-one correspondence between their elements. For example, the sets {1,2,3} and {3,2,1} are the same. Neither of them are the same as {1,2,1}.

- Math (Algebra) -
**Steve**, Monday, May 6, 2013 at 11:40am
assuming a<=b<=c

a = 1/c

b = 1/b

c = 1/a

a+b+c=2

We see that b=±1, so a+c=1 or 3

If b=1,

a+ 1/a = 1

a^2 - a + 1 = 0

2a = 1±√3 i

Nope

If b = -1,

a + 1/a = 3

a^2 - 3a + 1 = 0

a = (3±√5)/2

c = 2/(3±√5) = (3∓√5)/2

a^2+b^2+c^2 = (14+6√5)/4 + 1 + (14-6√5)/4 = 8

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