Roots and Differential Equations
What is the sum of all possible real numbers m such that the function
y = m
satisfies the differential equation
d x d y = y 5 − 9 5 y 4 − 3 7 7 8 y 3 + 5 2 3 4 0 y 2 + 8 3 3 4 9 6 y − 1 8 4 4 6 4 0 ?
The answer is 95.
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3 solutions
Haha, maybe 1 second is a bit of an exaggeration even for me. :D
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1 second is a huge exaggeration, you take way less.
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Really 1 second is a huge exaggeration but I took 5 seconds.
HAHAHA. That's awesome, thanks. :D
a noob here got it in 10 seconds @Finn Hulse you are a very fast problem solver "math fights"
The reason that this problem is so easy is because all you have to do is realize that if a function is constant, then d x d y = 0 always. So if we set that crazy mess of algebra equal to 0, we can solve for all possible m . And of course, to maximize speed in solving this, we can use Vieta's to find that the answer is just 9 5 .
But are you sure all 5 roots of the given equation are real, cause you said sum of all possible real numbers.
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You are right. Although all of the roots are in fact purely real (no imaginary part) in this case, it has yet to be proved, and so the question should probably be reworded as:
"What is the of the sum of all possible complex numbers m such that..."
I love how no one likes your solution but every one up votes Karan's. Btw, how r u supposed to factor this
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It's fine. My solution isn't great, which is probably why you missed how I mentioned that you use Vieta's formula for determining the sum of the roots of that polynomial.
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You cannot apply Vieta's directly, as Milly pointed out. This is a very common mistake made.
Given that, the title is inappropriate, and I have edited it.
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@Calvin Lin – Yes, I see what you mean. I'm not sure I should add a note saying "all roots to the above polynomial are real" because that might give it away...
Can u solve the eqn?
ROFL Answer is 95 (provided all the roots are real)
Well I take 6 second's in reading Question..... Finn Really You Are Very Faster Than Me...!!