does (2√x+2)²=4x+2 ?

[nancyy]

does (2√x+2)²=4x+2 ?

does (2√x+2)²=4x+2 is right? i got that in a hint in a question about radical equations.
here is a screen shot from the question and the hint http://postimg.org/image/l5elqht35/

doesn't (2√x+2)² = 4(x+2)=4x+8 ?


and another question, how much i need to know about radical equations in order to start learning calculus and linear algebra?

 

[Deleted member 4993]

does (2√x+2)²=4x+2 is right? i got that in a hint in a question about radical equations.
here is a screen shot from the question and the hint http://postimg.org/image/l5elqht35/

doesn't (2√x+2)² = 4(x+2)=4x+8 ? .... No

(2√x+2)² =

= 2² (x) +2*2*2√x + 2²

= 4x + 8√x + 4

and another question, how much i need to know about radical equations in order to start learning calculus and linear algebra?

You need to be very comfortable with "radical equations" to do well in Calculus.

 

[nancyy]

You need to be very comfortable with "radical equations" to do well in Calculus.

can i get some more explenation please? i usualy try to get answers for questions like that on symbolab.com and when i tried it there i got the same result as i tought
https://www.symbolab.com/solver/step-by-step/expand \left(2\sqrt{x+2}\right)^{2}/?origin=enterkey
it also mentioned the same exponent rule. so what is going on her?

That should be (2SQRT(x+2))^2
which equals 4(x+2) or 4x+8

Make sure you understand that.

i am right or wrong here?.

 

[Deleted member 4993]

does (2√x+2)²=4x+2 is right? i got that in a hint in a question about radical equations.
here is a screen shot from the question and the hint http://postimg.org/image/l5elqht35/

doesn't (2√x+2)² = 4(x+2)=4x+8 ?


and another question, how much i need to know about radical equations in order to start learning calculus and linear algebra?

Is it:

\(\displaystyle \displaystyle{\left(2\sqrt{x+2}\right )^2}\)

or

\(\displaystyle \displaystyle{\left(2\sqrt{x}+2\right )^2}\)

 

[nancyy]

Is it:

\(\displaystyle \displaystyle{\left(2\sqrt{x+2}\right )^2}\)

or

\(\displaystyle \displaystyle{\left(2\sqrt{x}+2\right )^2}\)

it was \(\displaystyle \displaystyle{\left(2\sqrt{x+2}\right )^2}\) as in the picture in the link i posted. i shouldn't trying to put it in the title, i don't even know how to put mathematical symbols in the post itself.

 

[stapel]

it was \(\displaystyle \displaystyle{\left(2\sqrt{x+2}\right )^2}\)

So do the squaring:

. . . . .\(\displaystyle \begin{align} \left(\, 2\, \sqrt{\strut x\, +\, 2\, }\, \right)^2\, &=\, \left(\, 2\, \sqrt{\strut x\, +\, 2\, }\, \right)\, \left(\, 2\, \sqrt{\strut x\, +\, 2\, }\, \right)

\\ \\ &=\, (2)\, (2)\, \left(\sqrt{\strut x\, +\, 2\, }\right)\, \left(\sqrt{\strut x\, +\, 2\, }\right)

\\ \\ &=\, (4)\, \left(\sqrt{\strut x\, +\, 2\, }\right)^2

\\ \\ &=\, (4)\, \lvert \, x\, +\, 2\, \rvert

\\ \\ &=\, \lvert\, 4x\, +\, 8\, \rvert \end{align}\)

 

[pka]

does (2√x+2)²=4x+2 is right? i got that in a hint in a question about radical equations.
here is a screen shot from the question and the hint http://postimg.org/image/l5elqht35/
doesn't (2√x+2)² = 4(x+2)=4x+8 ?

The correct answer is \(\displaystyle \Large{(2\sqrt{x+2})^2=4x+8}\) if \(\displaystyle \large x\ge-2\)

You see, if \(\displaystyle \large x=-3\) the LHS is not defined & the RHS is \(\displaystyle \large -4\)