Quadratics (again; please help!)
I don't understand how this:
3 ± 3√17
________
-12
Simplifies into this:
1 ±√17
________
-4
Hi Bailey,
Use the distributive property in reverse here.
Factor out the 3 in both terms of the numerator.
3 ÷ 3 = 1. Any number divided by itself equals 1.
The simplified result is just all that's left over
once the 3s are canceled out.
3 ± 3√17 3(1 ± √17) 3 1 ± √17 1 ± √17 -1 ± √17
_______ = __________ = ___ ∙ ______ = ______ = ________
-12 3(-4) 3 -4 -4 4
However, it would be unusual for the denominator to be left negative. That negative sign would most likely be absorbed into the numerator, as a matter of convention.
Wow. I am still very confused. Why would you divide? This has been the hardest thing in math I have done. Thanks for answering, though!
What you have to do is take the question into the factors of each of the numbers. Pei-Hsin Lin described it well, and I will do it differently, but based off of hers.
3±3√17
______
-12
Look at the factors, the low numbers that make up each number. The top ones are the lowest they can go, (17*1, 3*1, they are their factors) but 12 you can take down. It can be divided by 2, 12/2=6
So 6*2 is a factor. But can you go lower? divide 6/2, and it equals 3
So 3*2, and then add on the two from the first quotient. 3*2*2
All of these factors are still equal to 12, the original problem.
Now, put the factors into the problem, like so.
3±3√17
______
-3*2*2
You can cancel out the threes from the top part of the equation now, since there is a three on the top and bottom! Hope this helps! (And that it was not incorrect!)
Yours, Panzerkampfwagen
Ok. I have studied this so much, but I still cannot understand this last part. Thank you SO much for taking the time to answer (I mean this sincerely).
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