The condition that one root of the equation (1+m2)x2+2cmx+(c2−a2)=0  is reciprocal of the other is

The given equation is (1+m2)x2+2mxc+(c2−a2)=0 let the roots of the equation α  and 1α ∴  Product of the roots =α.1α=c2−a21+m2 ⇒1=(c2−a2)(1+m2) ⇒1+m2=c2−a2 Which is the required condition.