Question

please solve this
$please solve this question$

Answer 1

Given : (1 + m^2)x^2 + 2mcx + (c^2 - a^2) = 0.

On comparting with ax^2 + bx + c = 0, we get

a = (1 + m^2), b = 2mc, c = (c^2 - a^2).

Given that roots are equal.

= > b^2 - 4ac = 0

= > (2mc)^2 - 4(1+m^2)(c^2-a^2) = 0

= > 4m^2c^2 - 4(c^2 - a^2 + c^2m^2 - m^2a^2) = 0

= > 4m^2c^2 - 4c^2 + 4a^2 - 4c^2m^2 + 4m^2a^2 = 0

= > 4m^2a^2 - 4c^2 + 4a^2 = 0

= > m^2a^2 - c^2 + a^2 = 0

= > a^2(1 + m^2) - c^2 = 0

= > a^2 (1  + m^2) = c^2.


Hope this helps!