SOLUTION: 2) Is sqrt x^2 = x an identity (true for all values of x)? Explain answer please?

Algebra ->  Radicals -> SOLUTION: 2) Is sqrt x^2 = x an identity (true for all values of x)? Explain answer please?      Log On


   

Question 32745: 2) Is sqrt x^2 = x an identity (true for all values of x)? Explain answer please?
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
Is sqrt x^2 = x an identity (true for all values of x)? Explain answer please?
IN MATHS AS A RULE/COVENTION WE TAKE SQRT(A) AS THE POSITIVE VALUE ONLY.THAT IS SQRT(4) IS TAKEN AS +2 ONLY.,THOUGH -2 IS ALSO POSSIBLE,UNLESS OTHERWISE INDICATED.
CASE 1....X IS POSITIVE
SO WE GET LHS=SQRT.(X^2)=+X
RHS =+ X...
SO WE HAVE X=X WHICH IS AN IDENTITY AS IT IS TRUE FOR ANY VALUE OF X.
CASE 2......X IS NEGATIVE
SO WE GET LHS=SQRT.{(-X)^2}=SQRT.(X^2)=+X
RHS = -X...
SO WE HAVE X=-X WHICH IS NOT AN IDENTITY AS IT IS TRUE FOR ONLY X=0