Does there exist an interval I such that this system of equations has no solution?
k1(b1-a1)+a1 = k2(b2-a2)+a2
k1(b1^2-a1^2)+a1^2 = k2(b2^2-a2^2)+a2^2
k1(b1^3-a1^3)+a1^3 = k2(b2^3-a2^3)+a2^3
none of a1,b1,a2,b2 are equal
a1,b1,a2,b2 are on interval I
K1 and K2 are members of the reals
A proof would be appreciated if such an interval can be found or a proof of why no such interval can exist.
Thanks