Solving by Graphing and Using Algebra

[Mycroft]

One thing you should have added: by squaring a variable term, there is a chance of creating an extraneous value for the variable. The answers need to be checked every time. This is one time both solutions were valid, but that may not always be the case.

[fbjihqj]

squaring the quadratic equation may leads extra roots, so check always your answer.

[marcusgloder]

Hello everyone,

this is a very nice video. 👍 In order to be able to understand this at your leisure, I have written down the solution shown in the video in small steps:

√(x + 1) = x + 1 |²
x + 1 = (x + 1)²
x + 1 = x² + 2x + 1 | –1
x = x² + 2x | –x
0 = x² + x
x² + x = 0
x ‧ (x + 1) = 0

CASE 1
x₁ = 0

CASE 2
x + 1 = 0 | –1
x₂ = –1

I have one comment: right at the beginning the tutor squares on both sides. You can do that. Just know that you can get invalid results. This is because squaring on both sides is not an equivalent transformation. I think this has already been demonstrated on this channel using the example √(x) = –1. The example does not have a valid solution, but squaring both sides would produce the apparent solution x = 1.

Therefore, a control calculation actually has to be carried out if squaring occurs when converting the terms of an equation. This only is not necessary here because the graphical solution shows that both calculated solutions are valid.

Best regards
Marcus 😎

[harbinger]

Me (dramatically)- My knowledge grows! It grows!

[tzbq]

you can also substitute t=x+1 to not get extra solutions, now you see t=sqrt(t) so t is 0 or 1, x is -1 or 0

[jordanh]

Or if you're a quake programmer, sqrt(x) is just x plus a small constant

[weno]

if you square a root it becomes the absolute value of the terms under the root

[bornagainsaint]

Math genius !!!
I really enjoy watching him solve math problems !!!
Wasn’t it the Egyptians who created math solutions for math problems !!!

[SteveMathematician-thco]

When Squaring the root, you must get the absolute value of the variable under the square!

[isjosh]

I think most people know that sqrt(x) = x has sol 0, 1. So you could just do x+1 = 0 and x+1 = 1 and check for extraneous just in case

[Jayantimohantachhabi]

I am in 12th still love to watch his video😅😅❤❤❤❤....

[fahrenheit]

I think it's ideal if you emphasise the need to check the values after squaring. An approach like this could confuse people if they rely solely on algebra.

[pentameteriamb]

The best math teacher in the world. 😊

[shenglanliu]

This is too easy...(year8-year 9 maths)

[aquatic_marshan]

Can anyone recommend any books that give me high school level geometry and algebra problems?

[killianobrien]

Why not just let y=x+1, and sqrty=y trivially has solutions 1 and 0, then x = 0 or -1

[moeberry]

Graphing method is not good enough. You will not know if they intersect again or which function is above the other further down when x approaches infinity unless you use calculus. The better method is to solve using your second method. You also forgot to check for extraneous solutions but you got bailed out since both solutions worked.

[kevinphillips]

What level of math is this and where would any application be used?

[muslim]

Is it possible to x=-1? I mean no root for Zero

[hiyayahiyaya]

。。。。why not do this
√(x+1)=x+1
1=√(x+1) or √(x+1)=0
x=0 or x=-1