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

Answer:

Step-by-step explanation:

(a²+b²)x²-2(ac+bd)x+(c²+d²)=0

a=a²+b²

b= -2ac-2bd

c=c²+d²

D=b²--4ac

since the roots are equal D=0

0=b²-4(ac)

0=(-2ac-2bd)²-4{(a²+b²)(c²+d²)}

0=4a²c²+4b²d²+8abcd-4{a²c²+a²d²+b²c²+b²d²}

0=4a²c²+4b²d²+8abcd-4a²c²-4a²d²-4b²c²-4b²d²

0=8abcd-4a²d²-4b²c²

0=2abcd-a²d²-b²c²

0=a²d²+b²c²-2abcd

0=(ad-bc)²

0=ad-bc

ad=bc

a/b=c/d

hence proved

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