1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Finnish high school math problem.

  1. Dec 12, 2008 #1
    1. The problem statement, all variables and given/known data

    x1000 = x(2x)500-2998x2

    Okay. This is difficult. It is easy to notice that the solutions are x=0 and x=2 but how do you prove that? I have tried to resolve it in different ways with no luck at all. Maybe I haven´t noticed something. Any ideas? This is Finnish final exam puzzle from 1989...
  2. jcsd
  3. Dec 12, 2008 #2
    With high exponents and common bases, the trick is usually to factor.

    First, expand [tex](2x)^{500}[/tex] and then move all terms to one side. Factor out [tex]x^2[/tex] and note that x = 0 is a solution. What remains is a quadratic, which can be factored to get x = 2 as the only other solution.
  4. Dec 12, 2008 #3
    How do you know that it is clever to expand (2x)500? For example, I tried to expand x2.

    Is this the correct way?



    Okay, clearly x = 0 is a solution. But what´s the difference? There is still that exponent monster. How can I get that x = 2? I am not following...
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook