(l+m)²x²+2mcx+c²-a²=0 it has equal roots then show that c²=a²(l+m²)
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(1+m2)x2+2mcx+(c2-a2)=0
If this equation has equal roots
then
B2-4ac = 0
(2mc)^2-4(1+m^2)(c^2-a^2)=0 4m2c2-4(1+m2)(c2-a2)=0
4m2c2 = 4(1+m2)(c2-a2)
m2c2 = (1+m2)(c2-a2)
m2c2 = c2 - a2 + m2c2 - m2a2
0 = c2 -a2 - m2a2
0= c2-a2- m2a2
(1+m2)a2 = c2
HENCE PROVED
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