Question

If the roots of the equation (a²+b²)x²-2(ac+bd)x+(c²+d²)=0 are equal,
prove that a/b=c/d.

Answer 1

this is a math problem but
let \[p=a^2+b^2\]
\[w=c^2+d^2\]
G=ac+bd
so you are left with;
\[Px^2-2Gx+W=0\]
using viete's formula
\[x1+x2 = \frac{b}{a}, x1*x2 =\frac{a}{c}\] because of the -b
then use the fact that a/b=c/d, and a=(cb)d
substitute this in both solutions and you will be done.

Answer 2

I assumed that P,G and W are real numbers

Answer 3

In this case;
\[x1+x2 = \frac{2G}{P}, x1*x2 =\frac{P}{W}\]
because of the -2G