Question

What two numbers multiply to 196? If they do not add to 27, how do I create an equation that results in at least one extraneous solution?

Answer 1

What ?

Answer 2

haha, I'm trying by myself to come up with an equation that has an extraneous solution. I've gotten to the point where I need to figure out what two numbers multiply to 196, but add to 27.

Answer 3

But if there aren't any numbers that can do that, then I don't know how to make an equation with an extraneous solution. :/

Answer 4

ammm....

Answer 5

?

Answer 6

can u write your means ???

Answer 7

Here's an example of what I'm trying to do

Answer 8

I need to come up with an example like that one.

Answer 9

you would get an extraneous solution if you need to take the negative root

for example
\[ \sqrt{x^2} = - 2 \]
in these problems we normally only allow the positive value for the square root

Answer 10

So I would just have the root equal a negative number?

Answer 11

notice in your example they have
\[ \sqrt{1} - 7 =? -8 \\ 1 - 7 =? -8 \\ -6 ≠ -8\]
but if we took the negative square root , because you might think - is allowed in \( ±\sqrt{x} \)
you would get
\[ \sqrt{1} - 7 =? -8 \\ -1 - 7 =-8 \]

Answer 12

Ok, I think I understand where you are coming from. But how am I going to come up with an equation using that information?

Answer 13

we will get into trouble if we have
\[ \sqrt{x+a}=−x \]

because the left side will be positive (we only take the + square root)
but -x will be negative (assuming x is positive)

to find a "problem equation" we can work backwards:
square both sides
x+a = x^2
or
x^2 - x - a = 0

we want a quadratic with an x= positive and x= negative
(so that the positive x will be extraneous (see above)
for example
(x -2)(x+1) = 0
will have solution x= 2 and x= -1

expand to get
x^2 -x -2 = 0
add x+2 to both sides
x^2 = x+2
take the square root
\[ x=\sqrt{x+2}\]

I think this will have an extraneous solution

Answer 14

fixed a typo