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Radical and rational equations — Harder example

Watch Sal work through a harder Radical and rational equations problem.

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• lol you could've just stopped at m^2-12m+35 and did -b/a for the sum of roots, I solved this in 1 min
• shouldn't the answer be 5+7=12
• Yes. Well, sort of. The answer is 12. But the question is asking for the sum of the solutions, rather than the equation stating the sum. So, 12 is the correct answer.
• At first sight of such question, I would never think about doing all of that work!
• I have the exact same doubt about the square root of anything being either positive or negative. I'm getting a -7= sq root of 49
• Whoa, whoa, wait! @ he said that the square root of 16 is 4. But couldn't it also be negative 4? Same for the sqrt of 4 @. Couldn't that also be negative 2? How did he know to pick the positive square root?
• Hi! There can't be a negative number in a square root (It is possible but that is a whole different thing). -4 in a square root would be one of the complex numbers.
• why didnt we just square both sides in the beginning? why did we have to move the 3 to the other side first?
• The reason that Sal didn't square whole left side was because his goal in squaring was to get rid of the square root, which gets the equation into a form that we know how to work with. If we try and square the left side, when we expand it we still get a square root in our equation, which is a problem. This is because when you expand (a+b)^2, you get a perfect square trinomial a^2 + 2ab + b^2. The "2ab" term in this case would be 2(3)(sqrt(6m-26)), which in this case is ugly and has a square root in it, which makes things hard.
Generally, you want to eliminate square roots by isolating them on one side of the equation and then squaring both sides.
• couldn't have just used s=-b/a when turned into quadratic instead of making it a bit too long?
• no, because we should check for extraneous solutions.
• good luck everyone!! (i know that comment section is primarily for questions)
• Q) x-12 =(x+44)^1/2
What are the solutions X of the given equation?
A) 5
B) 20
C) -5 and 20
D) 5 and 20

I solved this question to get two values of x, that is, 5 and 20 and so I ticked option D). But in the book, the answer is given as option B). So when I put the values 5 and 20 in the original equation, I get -7= 49^1/2 (which is possible) but it is written in the book that it is not possible. Please explain