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\((l+m^2)x^2+2mcx+(c^2-a^2)=0\) সমীকরনের বীজদ্বয় সমান ।
\(\therefore\) নিরূপক=0
\(\therefore (2mc)^2-4(1+m^2)(c^2-a^2)=0\)
বা, \(4m^2c^2-4(c^2+c^2m^2-a^2-a^2m^2)=0\)
বা, \(4m^2c^2-4c^2-4c^2m^2+4a^2+4a^2m^2=0\)
বা, \(4c^2=4a^2+4a^2m^2\)
বা, \(c^2=a^2+a^2m^2\)

\(\therefore c^2=a^2(1+m^2)\) (প্রমাণিত)