SOLUTION: if a:b = b:c, show that a^2b^2c^2(1/a^2 + 1/b^2 + 1/c^2) = a^3 + b^3 + c^3.

Algebra ->  Proportions -> SOLUTION: if a:b = b:c, show that a^2b^2c^2(1/a^2 + 1/b^2 + 1/c^2) = a^3 + b^3 + c^3.      Log On


   

Question 1040720: if a:b = b:c, show that a^2b^2c^2(1/a^2 + 1/b^2 + 1/c^2) = a^3 + b^3 + c^3.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
The statement is not true.
Let a = 2, b = 3, and c = 4.5.
Then a:b = b:c, or a%2Fb+=+b%2Fc.
Now .
But...
a%5E3+%2B+b%5E3+%2B+c%5E3+=+2%5E3%2B3%5E3%2B4.5%5E3+=+126.125.
(And there's even a simpler example: a = 1, b = 2, and c = 4.)