Current location - Training Enrollment Network - Mathematics courses - 20 14 Math Examination for Junior Middle School Graduates in Shashi No.3 Middle School
20 14 Math Examination for Junior Middle School Graduates in Shashi No.3 Middle School
The reduction to absurdity assumes that all three equations have equal real roots,

Then 4b 2-4ac = 0, 4c 2-4ab = 0, 4a 2-4bc = 0.

That is, b 2 = ca, c 2 = ab and a 2 = BC.

(a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ca)

(a-b)^2+(b-c)^2+(c-a)^2=2(a^2+b^2+c^2)-2(ab+bc+ca)

=0

The contradiction that A, B and C are not equal is true if and only if A = B = C.

So the hypothesis is not true, and the original proposition is true.

This is?

?