Question

please please solve it​

Answer 1

Answer:

c^2=a^2(1+m^2)

Step-by-step explanation:

$दी \: गई \: समीकरण \\ (1 + {m}^{2} ) {x}^{2} + 2mcx + ( {c}^{2}- {a}^{2} ) = 0 .....(1) \\ \\ समीकरण (1)\: की \: तुलना a {x}^{2} + bx + c = 0 \: से \: करने \: पर \\ \\ a = (1 + {m}^{2} ) \: ,b = 2mc \: , c = {c}^{2} - {a}^{2} \\ अत: \: विविक्तकर \\ {b }^{2} - 4ac = 0 \\ (2mc) ^{2} - 4 \times (1 + {m}^{2} )( {c}^{2} - {a}^{2} ) = 0 \\ 4 {m}^{2} {c}^{2} - 4(1 + {m}^{2} )( {c}^{2} - {a}^{2} ) = 0 \\ 4( {m}^{2} {c}^{2} - (1 + {m}^{2} )( {c}^{2} - {a}^{2} ) = 0 \\ {m}^{2} {c}^{2} = (1 + {m}^{2} )( {c}^{2} - {a}^{2} ) \\ = {c}^{2} + {m}^{2} {c}^{2} - {a}^{2} - {a}^{2} {m}^{2} \\ {c}^{2} = {a}^{2} (1 + {m}^{2} )$

I hope this help you