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    • mathnerd_101

      FORUM REVIVE(hopefully)
      • mathnerd_101

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      mathnerd_101

      @excitedarmadillo-0 uhh :concern: are you ok?

      ANYWAYS, here's the non-i-want-to-die-and-i'm-a-masochist solution!
      Let us assume that

      $$a = x^2 - x - 2, b = 2x+1. $$

      Thus, the equation can be written as $$a^4 + b^4 = (a+b)^4 = a^4 + 4a^3b+6a^2b^2+4ab^3+b^4.$$

      Simplifying, we get $$2ab(2a^2 + 3ab+2b^2) = 0.$$

      Assuming that a=0, we get that $$x^2-x-2 = 0,$$ thus x = -1 or x = 2, which are the solutions of the equation.

      Assume now that b=0, we get that $$x = -\frac{1}{2}.$$

      Finally, assume that ab does not equal 0, then we get $$2a^2+3ab+2b^2 = 0.$$ As this is a quadratic equation in a, the discriminant is $$-7*b^2<0.$$

      Thus, this equation has no solution, meaning that we have 3 solutions: $$-1, -\frac{1}{2}, 2 \blacksquare$$

    • S

      AMC 8 Question
      • superdog

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      mathnerd_101

      @superdog I'm getting half, but it appears, on the test doc, that half isn't an answer choice, so I'm not sure anymore...

    • S

      Doesn’t 11 have two 1s ?One on the tens digit and one on the units digit? Why does the answer says that 11only have 1s on the tens digit?
      • smilingtadpole 1

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      mathnerd_101

      @smilingtadpole-1 In this problem, we do not care whether 11 has one or two 1s. What matters is the fact that 11 contains a 1. When you solved this problem, you assumed that because 11 had two ones, it should be counted twice, which is incorrect. I hope this helps!(also charge your device lol)

    • M

      1991 AMC 8 Question 16
      • magnificenthorse

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      M

      Thanks for the explanation. I guess I didn’t think that the card had numbers on both sides. But it makes sense now.

    • R

      Type in as many math problems as you can find
      • reliabledove

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      E

      -1x-2+3-4+(5x6-7^2)- -18=?

    • V

      In This Math Game, How Many Results Can You Get?
      • versatilemole

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      lucky_ducky1

      @versatilemole i could give as many solutions as i can to this problem, and then people can add on solutions and count how many ways we can make 100.

    • R

      A trick about blahblah^0
      • reliabledove

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    • R

      How do you vote for somebody?
      • reliabledove

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    • M

      Mathcounts National Sprint Round Please Help
      • meticulousbunny

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      mathnerd_101

      Not really 🙂 Notice how Elmo has three blocks. It wouldn't be $$\binom{9}{3}$$ because you use a separate block every time so you would have to choose the first block, then the second, and so on. Try to see where you can go from there 😉

      Note: Sorry this is so late I doubt you're active on this forum anymore.

    • R

      Sorry about my previous post, I made a mistake
      • reliabledove

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    • R

      My little sister said this is how you solve adittion
      • reliabledove

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    • T

      Expanding my question on LS#17 M3
      • TheConfusedOne

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      T

      @knowledgeabledog Thanks!

    • B

      Some interesting fill in puzzle
      • boldsidewinder 0

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      B

      @rationaltiger Correct!

    • A

      An Grade 4 Math Olympiad problem
      • altruisticgoat

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      T

      =1+11+111 times 68
      =12+548
      =560

    • P

      Random(but interesting) problem
      • Perceptiveeagle

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    • M

      An interesting problem (3)
      • modestwallaby

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      C

      24+3/4(24)(2)+(3/4^2)(24)(2)+(3/4^3)(24)(2)+.....
      (The x2 is because the ball drops the same distance up and down)

      This is an infinite arithmetic sequence.

      Let S = 3/4(24)(2)+(3/4^2)(24)(2)+... = 36+(3/4)(36)+(3/4^2)(36)+....
      So 4/3S=48+36+(3/4)(36)+....
      So 4/3S-S=1/3S=48
      So S=144
      So S+24=168?

    • M

      An interesting problem (2)
      • modestwallaby

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      M

      MISSPELL has 8 letters with 2 S’s and two L’s. 8!/(4!2!) = 10,080 arrangements, but one of these is the correct spelling, so there are 10,079 misspellings in total.

    • M

      An interesting problem
      • modestwallaby

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    • M

      Mathcounts National
      • meticulousbunny

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    • M

      Mathcounts problems help
      • modestwallaby

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