Question

if roots of equation (a square +b square) x square +2(bc-ad) x+c square +d square =0 are equal then show that ac+bd=0​

Answer 1

Answer:

⟹[2(bc−ad)

]

2

−4(

a

2

+

b

2

)(

c

2

+

d

2

)=0

⟹[2(bc−ad)]2−4(a2+b2)(c2+d2)=0

⟹4(

b

2

c

2

+

a

2

d

2

−2abcd)−4

a

2

c

2

−4

a

2

d

2

−4

b

2

c

2

−4

b

2

d

2

=0

⟹4(b2c2+a2d2−2abcd)−4a2c2−4a2d2−4b2c2−4b2d2=0

⟹−8abcd−4

a

2

c

2

−4

b

2

d

2

=0

⟹−8abcd−4a2c2−4b2d2=0

⟹2abcd+

a

2

c

2

+

b

2

d

2

=0

⟹2abcd+a2c2+b2d2=0

⟹(ac+bd

)

2

=0

⟹(ac+bd)2=0

Explanation: