Question

if the roots of the equation (a square+b square) x square -2 b (a+c) x+(b square +c square)=0 are equal then​

Answer 1

Step-by-step explanation:

${b}^{2} - 4ac = 0 \\ ( - 2b {(a + c))}^{2} -4( {a}^{2} + {b}^{2})( {b}^{2} + {c}^{2}) = 0 \\ 4 {b}^{2} ( {a}^{2} + 2ac + {c}^{2}) - 4( {a}^{2} {b}^{2} + {a}^{2} {c}^{2} + {b}^{4} + {b}^{2} {c}^{2}) = 0 \\ 4 {a}^{2} {b}^{2} + 8 {b}^{2}ac + 4 {b}^{2} {c}^{2} - 4 {a}^{2} {b}^{2} - 4 {a}^{2} {c}^{2} - 4 {b}^{4} - 4 {b}^{2} {c}^{2} = 0 \\ 8 {b}^{2}ac - 4 {a}^{2} {c}^{2} - 4 {b}^{4} = 0 \\ 2 {b}^{2}ac - {a}^{2} {c}^{2} - {b}^{4} = 0 \\ {b}^{4} - 2 {b}^{2}ac + {a}^{2} {c}^{2} = 0 \\ {( {b}^{2}) }^{2} - 2 {b}^{2}ac + {(ac)}^{2} = 0 \\ {( {b}^{2} - ac)}^{2} = 0 \\ {b}^{2} - ac = 0 \\ {b}^{2} = ac \\ a \: b \: c \: in \: gp \\ = = = = = = =$

Answer 2

Answer:

Step-by-step explanation: