Question

(a^2+b^2)x^2-2(ac+bd)x+c^2+d^2)=0 Have equal roots ,prove that a/b=c/d

Answer 1

equal roots means D=b^2-4ac=0
use this here ,
{2 (ac+bd)}^2-4 (a^2+b^2)(c^2+d^2)=0

4 {a^2c^2+b^2d^2+2abcd}-4(a^2c^2+a^2d^2+b^2c^2+b^2d^2)=0

=>-a^2d^2-b^2c^2+2abcd=0

=>{(ad)^2+(bc)^2-2 (ad)(bc)}=0

=>(ad-bc)^2=0

=> ad=bc

=> a/b=c/d
hence proved