(√x+2)=-4 Solve this equation

[znick46]

Hi,

(√x+2)=-4 -Please note the square root sign covers the x and 2- Solve this equation

My Answer: x=14

Textbook Answer: No solution

I'm confused why am I wrong? Please explain

 

[pka]

(√x+2)=-4 -Please note the square root sign covers the x and 2- Solve this equation
My Answer: x=14. Textbook Answer: No solution

The textbook is correct. \(\displaystyle (\forall x\ge 0)[\sqrt x \ge 0]\). So it is impossible for \(\displaystyle \sqrt{x+2}=-4\)

 

[znick46]

[FONT=MathJax_Main]If you inserted 14 for x it checks out okay, or please find how i'm checking the answer wrong to correct me.

[/FONT]√x+2= -4
√14+2=-4
√16=-4
square both sides
16= +16

PS: What is [FONT=MathJax_Main]∀?[/FONT]

 

[pka]

√x+2= -4
√14+2=-4
√16=-4
square both sides
16= +16
PS: What is [FONT=MathJax_Main]∀?[/FONT]

Someone has lied to you. Or else you have not paid attention in class.
\(\displaystyle \sqrt{16}=4\) BUT \(\displaystyle \sqrt{16}\ne -4\)

 

[znick46]

I understand your saying

√16 doesn't equal -4

I don't understand why, and that's what i'm curious about. Can you please explain?

 

[Deleted member 4993]

I understand your saying

√16 doesn't equal -4

I don't understand why, and that's what i'm curious about. Can you please explain?

By definition, √(16) = 4

However solution of the equation

x² = 16

is

x = ± 4

 

[Quaid]

[FONT=MathJax_Main]
[/FONT]PS: What is [FONT=MathJax_Main]∀?
[/FONT]

It means "for all".

Here's a symbol reference site: http://www.rapidtables.com/math/symbols/Logic_Symbols.htm

---

The symbol \(\displaystyle \sqrt{c}\) always represents the positive square root of c

We call this "The Principle Square Root".

If you need to express the negative root, then write \(\displaystyle -\sqrt{c}\)

Cheers :cool:

 

[JeffM]

I understand your saying

√16 doesn't equal -4

I don't understand why, and that's what i'm curious about. Can you please explain?

\(\displaystyle (- 4) * (- 4) = 16 = 4 * 4.\)

So TWO distinct numbers when squared = 16. Which number is meant by \(\displaystyle \sqrt{16}?\)

It is a convention that \(\displaystyle \sqrt{a} \ge 0.\)

The other number that when squared equals a is identified as \(\displaystyle - \sqrt{a}.\)

Formally, this is established by the following definition.

\(\displaystyle \sqrt{x^2} \equiv |x|\ for\ all\ x \in \mathbb R.\)

This means that \(\displaystyle \sqrt{(- 4)^2} = 4 = \sqrt{4^2}.\)

When you see solutions to quadratic equations such as \(\displaystyle x = 1 \pm \sqrt{5}\),

the reason for the plus/minus sign is to show both the non-negative value denoted by the square root symbol and the negative value denoted by minus the square root symbol.

 

[lookagain]

[FONT=MathJax_Main]If you inserted 14 for x it checks out okay,
or please find how i'm checking the answer wrong to correct me.[/FONT]

√x+2= -4 \(\displaystyle \ \ \ \) *

√14+2=-4\(\displaystyle \ \ \ \) *

√16=-4

square both sides \(\displaystyle \ \ \ \)

No, squaring both sides is not valid when checking.
16= +16

znick, do not type these type * anymore without putting required grouping symbols around the radicands.

Here's what those steps for checking x = 14 above needed to look like, for instance:

√(x + 2) = -4

√(14 + 2) = -4?

√(16) = -4?

\(\displaystyle 4 \ne -4\)