No More Extraneous Roots CONFUSION - Radical Equations

[@dziprick3204]

Old math books are the best. No 'commercials' or other distractions from the content. Math teacher here, and also a math book collector. v

[@themasterrogerdelgado]

I'm enjoying these - especially since I'm studying to be a high school math teacher.

[@wernerviehhauser94]

I wish you luck, but brace yourself for impact. Teaching highschoolers nowadays does not compare to what our teachers had to do.

[@brianjenkins3133]

The confusion in the algebraic solution potentially lies in the fact the radical (which only has One principle real and positive solution) is converted to a polynomial (to transform the radical into a solvable algebraic expression) which creates a new expression with a minimum of Two Solutions.

[@warblerab2955]

Thank you!

[@MathCuriousity]

you shouldn't say the radical function is not a function because it doesn't pass the vertical line test. It is still a FUNCTION.

[@tamarleigh]

It’s still a RELATION. A function has a single consistent output for each input.

[@MathCuriousity]

@@tamarleigh interesting! I apologize but what is the difference between a function, a relation, and an “operator” ?!

[@MathCuriousity]

@@tamarleigh but what is the difference between a FUNCTION and an OPERATION?! Help me!

[@tanmay5070]

​​@@MathCuriousity in a relation, for one 'x' you could possible get more than one values which are linked with 'x' example of a relation is equation of circle, (x² + y² = a²) this equation represents a circle with center of the circle at the origin and radius = a. Clearly, for one value of x, you will get two values of y. Hence, it is NOT a function for functions, for any value of x belonging in the domain of the function, you will only get a single value of y. for example, we have (y = ax) it's a straight line, with slope = a. clearly, for any value of x belonging to its domain (set of real numbers in this case) we only get one value of y which equals a times x. the reason why square roots are called functions: ( root (x) )² = |x| you see, when you square (root x) it equals |x| and not x. again, if you consider |x|, it is a function ==> for any value belonging to its domain, you will only get a single value of y so, for any value of x belonging to the domain of (root x) i.e. (set of all non negative real numbers) you only get one value of y hope that helps. feel free to ask if you didn't understand something!