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sum of the root of equation |x-3|^2+|x-3|-2=0 is equal to

July 28, 2018 0
open vertical bar x minus 3 close vertical bar squared plus open vertical bar x minus 3 close vertical bar minus 2 equals 0 left parenthesis x minus 3 right parenthesis equals 0 x equals 3 c a s e space i comma space w h e n space x greater or equal than 3 open vertical bar x minus 3 close vertical bar squared plus open vertical bar x minus 3 close vertical bar minus 2 equals 0 left parenthesis x minus 3 right parenthesis squared plus left parenthesis x minus 3 right parenthesis minus 2 equals 0 x squared plus 9 minus 6 x plus x minus 3 minus 2 equals 0 x squared minus 5 x plus 4 equals 0 x squared minus 4 x minus x plus 4 equals 0 x left parenthesis x minus 4 right parenthesis minus 1 left parenthesis x minus 4 right parenthesis equals 0 left parenthesis x minus 4 right parenthesis left parenthesis x minus 1 right parenthesis equals 0 x equals 4 space space space a n d space x equals 1 b u t space c o d i t i o n space i s space x greater or equal than 3 s o space o n l y space x equals 4 space i s space s a t i s f y s o space o n l y space o n e space r o o t space e x i t s. c a s e space I I minus space w h e n space x less than 3 open vertical bar x minus 3 close vertical bar squared plus open vertical bar x minus 3 close vertical bar minus 2 equals 0 left parenthesis x minus 3 right parenthesis squared plus left parenthesis negative left parenthesis x minus 3 right parenthesis right parenthesis minus 2 equals 0 x squared plus 9 minus 6 x minus x plus 3 minus 2 equals 0 x squared minus 7 x plus 10 equals 0 x squared minus 5 x minus 2 x plus 10 equals 0 x left parenthesis x minus 5 right parenthesis minus 2 left parenthesis x minus 5 right parenthesis equals 0 left parenthesis x minus 5 right parenthesis left parenthesis x minus 2 right parenthesis equals 0 x equals 5 space space space a n d space x equals 2 b u t space c o n d i t i o n space i s space x less than 3 h e r e space x equals 5 space space space a n d space x equals 2 space n o t space s a t i s f y h e n c e space o n l y space o n e space r o o t space x equals 4 space e x i s t s a n d space a l s o space s u m space o f space t h e space r o o t space i s space 4 o p t i o n space B space i s space c o r r e c t
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