Question

if the roots of the equation (a^2+b^2)x^2-2b(a+c)x+(b^2+c^2)=0 are equal, find the relation bw a, b and c

Answer 1

$( {a}^{2} + {b}^{2} ) {x}^{2} - 2b(a + c)x + ( {b}^{2} + {c}^{2} ) = 0 \\ given \: roots \: are \: equal \\ delta = 0 \\ {( - 2b(a + c))}^{2} = 4( {a}^{2} + {b}^{2} )( {b}^{2} + {c}^{2} ) \\ = > {(ab + bc})^{2} = ( {a}^{2} + {b}^{2} )( {b}^{2} + {c}^{2} ) \\ = > 2a {b}^{2} c = {a}^{2} {c}^{2} + {b}^{4}$
hope it helps