Are A = {x : x – 5 = 0} and B = {x : x is a positive  integral root of the equation x2 - 2x - 15} equal sets?

Asked by Topperlearning User | 21st Apr, 2016, 08:05: AM

Expert Answer:


G i v e n space t h a t space A equals open curly brackets x colon x minus 5 equals 0 close curly brackets
T h u s comma space A equals open curly brackets 5 close curly brackets
C o n s i d e r space t h e space s e t space B equals open curly brackets x colon x space i s space a space p o s i t i v e space space i n t e g r a l space r o o t space o f space t h e space e q u a t i o n space x squared minus 2 x minus 15 close curly brackets
F a c t o r i z i n g space t h e space g i v e n space e q u a t i o n comma space w e space h a v e comma
x squared minus 2 x minus 15 equals 0
rightwards double arrow x squared minus 5 x plus 3 x minus 15 equals 0
rightwards double arrow x open parentheses x minus 5 close parentheses plus 3 open parentheses x minus 5 close parentheses equals 0
rightwards double arrow open parentheses x plus 3 close parentheses open parentheses x minus 5 close parentheses equals 0
rightwards double arrow x equals negative 3 space o r space x equals 5
S i n c e space x equals negative 3 space i s space n o t space a space p o s i t i v e space i n t e g r a l space r o o t comma space w e space h a v e comma space B equals open curly brackets 5 close curly brackets
T h u s comma space A equals B

Answered by  | 21st Apr, 2016, 10:05: AM