Each of a, b, c, d, e and f is a positive integer satisfying this system of equations:
a-2 + b-2 + c-2 + d-2= e-2, and:
1/a+ 1/b+ 1/c+ 1/d= f-2
Determine the smallest value of f. What are the next three smallest values of f?
then we have
thus we want
and we also need
a^2=4e^2 since a,e>0
thus for any postive f we can find a,b,c,d,e satifying the equations.
thus the smallest value of f is 1, and the next 3 are 2,3,4.
Posted by Daniel
on 2011-09-09 10:54:06