Recent content by cupcakes

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    What is the factorization of x^4-2x^3+3x^2-2x+1?

    Exactly. After expanding and canceling out we have: 7x6 - 21x5 + 35x4 - 35x3 + 21x2 - 7x. First I divided by (7x). Then I realized (x-1) is a factor (since x=1 is a zero). After long division I have: (7x)(x-1)(x4 - 2x3 + 3x2 - 2x + 1)
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    What is the factorization of x^4-2x^3+3x^2-2x+1?

    I think I'm very close to solving it. I substituted y= (1-x) in the first equation and expanded. Then I factored that. However I don't know how to factor the last term. x4-2x3+3x2-2x+1 WolframAplha say it can be factored into (x2-x+1)2. I just need to figure out how to factor that into this...
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    What is the factorization of x^4-2x^3+3x^2-2x+1?

    Homework Statement Given: x7 + y7 =1 x + y = 1 Find the integer value(s) of (x-y)2. Homework Equations The Attempt at a Solution I thought of substituting for y and then finding the rational roots but then I realized x and y don't have to be rational numbers for (x-y)^2 to be an...
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    Solve Inequality Homework: A Hint Needed

    Homework Statement To prove the inequality (attached) Homework Equations The Attempt at a Solution I tried factoring out a 2 from each of the even terms in the denominator. This allowed me to cancel out all the terms (odd) on the numerator up to 1005. Leaves me with...
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    Can Inequality with Factorial Be Proven without Induction?

    I've solved it. :smile:
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    Can Inequality with Factorial Be Proven without Induction?

    I forgot to mention that the problem states that it must be proven without using induction. :( Thanks Sammy :smile: Does anyone have any other idea or hint that does not involve induction?
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    Can Inequality with Factorial Be Proven without Induction?

    Homework Statement \frac{1^2*3^2*5^2...(2n-1)^2}{2^2*4^2*6^2...(2n)^2}<\frac{1}{2n+1} Edit: Must be proven without using induction. Homework Equations The Attempt at a Solution I understand the LHS is the same thing as \frac{(2n-1)!}{(2n)!} And (2n)! = k!2^k & (2n-1)! =...
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    Use standard identities to express

    that seems right to me. However I'd keep sin(π/3) as \frac{\sqrt{3}}{2}. Edit: I didn't see rock.freak667's reply.
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    Don't understand this problem (Permutations, I think)

    Thank you, I finally understand what it means. It may be easy for you but I've never learned permutations or anything like this. This problem is not course material, just something I came across. Alright that makes sense. Since we can prove that there will always be at least one even factor...
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    Don't understand this problem (Permutations, I think)

    From what Ray said, I gathered that we substitute arrangements of the 2011 numbers. However, if I understand you correctly, you're saying that we substitute the integers themselves. I'm confused... Edit An attempt at the problem: ODD + ODD = EVEN ODD + EVEN = ODD...
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    Don't understand this problem (Permutations, I think)

    So let's say instead of 2 to 2012 its from 7 to 12. would one possible arrangement be {10,12,9,7,8,11} → 101297811 ? if that's so I'm guessing there are much more possible arrangements of 2 to 2012 than 2012. Yet the product only has up to a2012. So is this some sort of probability question...
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    Factor Expression: A2+B2 from 3[√3+√5+√7]2

    How did I not notice that?! :smile: That works perfectly Mark. Thanks to everyone for their help.
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    Don't understand this problem (Permutations, I think)

    Homework Statement Please see attached image. Homework Equations The Attempt at a Solution I don't understand the problem at all. Can someone explain to me what the problem is stating, more precisely what an arrangement is? An example would be nice. Thanks.
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    Raise complex number using De Moivre - integer only?

    I may be wrong but in mathematics, n is used to denote an integer by convention.
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    Factor Expression: A2+B2 from 3[√3+√5+√7]2

    Maybe it's because I forgot to mention that A & B may contain roots. I think it's possible because it is an assigned question. But I'm stuck...