Question

1/x+p + 1/x+q = 1/r​

Answer 1

Answer:

x+p

1

+

x+q

1

=

r

1

⇒(x+q+x+p)r=(x+p)(x+q)

⇒2xr+(p+q)r=x

2

+(p+q)x+pq

⇒x

2

+(p+q−2r)x+pq−pr−qr=0

As roots are equal in magnitude and opposite the sign

Then sum of roots =0

⇒p+q=2r

Hence, product of roots

pq−pr−qr=pq−

2

(p+q)

2

=−

2

p

2

+q

2

Answer 2

Ans= -(p2 + q2/2 = product of roots