Extraneous solutions to radical equations | Algebra I | Khan Academy

Extraneous Solutions to Radical Equations

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Algebra I on Khan Academy: Algebra is the language through which we describe patterns. Think of it as a shorthand, of sorts. As opposed to having to do something over and over again, algebra gives you a simple way to express that repetitive process. It's also seen as a "gatekeeper" subject. Once you achieve an understanding of algebra, the higher-level math subjects become accessible to you. Without it, it's impossible to move forward. It's used by people with lots of different jobs, like carpentry, engineering, and fashion design. In these tutorials, we'll cover a lot of ground. Some of the topics include linear equations, linear inequalities, linear functions, systems of equations, factoring expressions, quadratic expressions, exponents, functions, and ratios.

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[BarfBag]

Your voice just seems really friendly, and you're easy to follow. Thanks for the help.

[medievalmusiclover]

Love your black scream is very relaxing. :D

[sadafbenaf]

I always was thinking WHY an answer is extraneous, you solved it. Many thanks! I also wonder that what kind of equations (I.e. Quadratic, abs-value, cubic, etc) could have extraneous solutions? Should I ALWAYS check my answers after I solve them?

[Gee]

You are so good with your videos. If I have any questions after my high school teacher confused me about, you clear them up, (if you have talked about them). 5*ed all of your videos that I have seen so far.

[touhami]

Sqrt(A)=B <==>
B>=0 ===> D of validity
A=B^2 in D

Sqrt(x)=2x-6 <===>
2x-6>=0 ===> x>=3 : D of validity
x=(2x-6)^2 ===> x=2.25 or x=4
Only 4 is in D so S={ 4 }.

[GothicElf]

In my math class, we learned to factor the trinominal, then solve the factors for 0. In this case, the factors are (4x-9)(x-4). Solving 4x-9=0 results in x=9/4, which is equivalent to 2.25. Solving x-4=0 results in x=4. Maybe I am just familiar with this method, as it is the same method we've been using in factoring, solving quadratics, solving inequalities, etc, but it seems a lot less complicated to me than the way you are explaining in this video. Regardless, the results are the same, so either method is equally valid.

[calculusfan]

Here's a question: What about when you solve the following equation:
sqrt(5x-1)=sqrt(9x+63). After squaring both sides and solving, you get x=-16. When you check the solution, you get sqrt(-81)=sqrt(-81), so both sides are equal, but they are an imaginary value. It appears to check, but the graphs of the functions on each side do not cross at x=-16 because of their restricted domains. How do you explain this?

[FAN]

Thanks for the help! Very easy to follow!

[raygodinez]

thanks much for the explanation! the plus or minus in the quadratic formula left always left me with a funny feeling. but know I understand (i think): is it safe to say the calculation is only taking the positive square of x into consideration? if so, why have the plus and minus in the quad formula (besides its use in word problems looking for a range of x)?

[TheBigCheezeIt]

Woah that was cool! Keep it up Sal! I never have any questions when I'm done with your videos!

[skusaid]

Best as always sir. Love from Kashmir!☺

[NoobGamer-uhkc]

You just saved me man, this is so easy, now I see that the problem is not me is my teacher. Thank you

[mrs.negative]

I’m so lost and confused on the formula :c like how did you get the square for 25? Why is 25x b ? and why can’t 4x be ???

[kamrunnaharrani]

Life saviour before exams: sal sir

Thanks a lot sir!

[roidroid]

@warlockzombie best to start further back in the series where quadratic formulas were introduced

[PC-yvkq]

Please explain why the square root of 2.25 cannot be equal to -1.5 wherein it can have two possible values: 1.5 and -1.5.

[dxlkey]

Great worlk man! What software are you using for for digital chalkboard?

[TheBlackShadowHawk]

1:24 why would you multiply (2x -6) = -12x, when they are not like terms? Would you only square a radical if it is not a perfect square?

[droshafa]

can't you just specify that the sqrt(x) must be > or = 0 for the squared version of the equation to keep it consistent with the original, the same way we do it when we specify that x must not result in zero in the denominator?

[MrDevin]

This guy is so smart, love him more than a teddy bear from "build-a-bear" workshop