Question

If the equation (1+m2)n2x2+2mncx+(c2-a2)=0 of x has equal roots, prove that c2 = a2(1+m2)

Answer 1

Answer:

Step-by-step explanation is in picture:

Answer 2

Step-by-step explanation:

a=n²(1+m²)=n²+m²n²

b=2mnc

c=c²-a²

as the equation have equal roots;

b²-4ac=0

(2mnc)²-4[ (n²+m²n²)(c²-a²) ]=0

4m²n²c²-4(m²n²c²+n²c²-a²n²-m²n²a²)=0

4m²n²c²-4m²n²c²-4n²c²+4n²a²+4m²n²a=0

4n²a²-4n²c²+4m²n²a²=0

4n²(a²-c²+m²a²)=0

a²-c²+m²a²=0

a²+m²a²=c²=0

a²(1+m²)=c²-> thus proved

hope this answer is helpful..