Question

Create an equation that results in at least one extraneous solution. Work through your equation, justify each step, and explain how the solution is extraneous.

Answer 1

One type of equation that often gives extraneous solutions is one that contains absolute value. You could get a solution where the absolute value equals a negative number, etc.

Answer 2

An example would be |x|=-1, absolute value is always positive, so any solution you come up with wouldn't work
this will help you understand
http://hotmath.com/hotmath_help/topics/extraneous-solutions.html

Answer 3

Thanks @miryluslinares ! I've got a couple more questions for ya if you don't mind :)

Using the properties of exponents and radicals, design at least three different equivalent forms of x². You must show how each one can be simplified back to x² in two or more steps. Stretch your mind and get creative! Keep in mind that something too simple, like x • x would not be acceptable since it takes only one step to convert it to x².

Answer 4

One form is the square root of x to the fourth power:
(x^4)^1/2

Another form is the fourth root of x to the eighth power:
(x^8)^1/4

Another form is the eighth root of x to the sixteenth power:
(x^16)^1/8

Each one can be simplified to x^2 by multiplying the exponent within the parenthesis with the external exponent.

Answer 5

Wow you're good lol Thanks so much! Just one more :)

Substitute your birthday into the equation \[\sqrt{x-y} + m = d\] where y is the last two digits of your birth year, m is the month, and d is the day. If you were born on 7/10/1856 like Nikola Tesla, your equation would be \[\sqrt{x-56} + 7 = 10\] Solve for x and identify if it is an extraneous solution.

Answer 6

im sorry i dont know how to do this one:(

Answer 7

Oh, ok thanks anyway though!