Question

if the sum of the root of the equation px2+qx+r=0 is equal to sumo the squares of their reciprocal show that qr2,rp2, pq2 are in AP

Answer 1

a/b = a^2/ab (multiplying Nr & Dnr of a/b with a).

So 1st term is sqrt(a^2/ab) = a/sqrt(ab) —————————- (1)

b/a = b^2/ab (multiplying Nr & Dnr of b/a with b)

2nd term, therefore is sqrt(b^2/ab) = b/sqrt(ab) —————(2)

So sum of first two terms = (a+b)/ sqrt(ab) ———————-(3)

Now, a+b = -q/p ab q/p - substituting in (3), we get

= -(q/p) / sqrt (q/p) = - sqrt (q/p)

So LHS is - sqrt(q/p) + sqrt (q/p) = 0

Hope This Helps :)