Bootcamp QR confusion ...

[Prima Donna]

So there is a problem ( # 7) on bootcamp QR test 7 that I got wrong and the explanation makes no sense to me. Idk if I can post what the question is asking but I guess I will until someone says it's copyright or something.

Question says: what is the solution set to the following equation: x +2 = ( 5x + 16 ) ^ (1/2)

basically after you solve that you get x^2 - x - 12 = 0
( x-4 ) (x +3 ) = 0
x = 4 x = -3

It says that only +4 is the right answer because the -3 basically messes with the 'square root has to be a positive number' but when you plug -3 back into the equation it does not give you a negative number under a square root ? I thought the correct answer was (-3,4) but it says it is just (4).

Thanks for any help.

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[MickeyMug]

Don't forget that when you raise something to the (1/2) power, it's basically like taking the square root of it.
If you plug -3 back into the equation, you'll get:
(-3) + 2 = [ 5(-3) + 16 ] ^ (1/2)
-1 = (-15 + 16)^(1/2)
-1 = (1)^(1/2) -> -1 = 1
We know that -1 does not equal +1 therefore -3 is not an answer choice.

 

[Prima Donna]

Don't forget that when you raise something to the (1/2) power, it's basically like taking the square root of it.
If you plug -3 back into the equation, you'll get:
(-3) + 2 = [ 5(-3) + 16 ] ^ (1/2)
-1 = (-15 + 16)^(1/2)
-1 = (1)^(1/2) -> -1 = 1
We know that -1 does not equal +1 therefore -3 is not an answer choice.

Ohh so it just has to do with plugging back in and making sure the equation makes sense (ie the number on the left side = the number on the right) ?

 

[artist2022]

-1 = (1)^(1/2) -> -1 = 1

But when you take the square root of any number, you get both positive and negative values. How do you know you have to look at only the positive one? The square root of 1 is both +/- 1...

 

[MickeyMug]

Ohh so it just has to do with plugging back in and making sure the equation makes sense (ie the number on the left side = the number on the right) ?

Yes that is correct!

 

[MickeyMug]

But when you take the square root of any number, you get both positive and negative values. How do you know you have to look at only the positive one? The square root of 1 is both +/- 1...

Yeah this can get confusing sometimes. In math, when you explicitly see a square root sign (or something raised to the 1/2 power in this case) in the equation, it always refers to the positive root. however, when you have an equation, let's say, (x^2 = 4) and they ask you to solve for x, you can square root both sides, or you can subtract 4 from both sides and get (x^2 - 4 = 0), there you can factor out the equation and get [(x + 2)(x - 2) = 0] which means that (x = -2, +2)

 

[artist2022]

In math, when you explicitly see a square root sign (or something raised to the 1/2 power in this case) in the equation, it always refers to the positive root

Ooooooh okay I didn't know this, thank you lots

 

[Prima Donna]

Yes thank you !

 

[DAT Destroyer]

Ohh so it just has to do with plugging back in and making sure the equation makes sense (ie the number on the left side = the number on the right) ?

The best way to solve this type of problems is simply check which number will work ( if the numbers are nice ). If you solve it, make sure to check both answers. In this case x=-3 doesn't work. It's called an erroneous solution.
This also applies to problems involving absolute values and logs.