If the equation (1+m square)x square + 2mcx + (c square - a square) = 0 has two equal roots, prove that c square = a square ( 1 + m square).
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(1+m) x^2+2mcx +(c^2-a^2)=0
because roots are equal
so, D=b^2-4ac=0
(2mc)^2-4 (c^2-a^2)(1+m^2)=0
=> 4m^2c^2-4c^2-4m^2c^2+4a^2+4a^2m^2=0
=> c^2=a^2+m^2a^2
=> c^2=a^2 (1+m^2)
because roots are equal
so, D=b^2-4ac=0
(2mc)^2-4 (c^2-a^2)(1+m^2)=0
=> 4m^2c^2-4c^2-4m^2c^2+4a^2+4a^2m^2=0
=> c^2=a^2+m^2a^2
=> c^2=a^2 (1+m^2)
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