1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    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!

Prove Existence Unique Real Solution

  1. Mar 22, 2014 #1
    1. The problem statement, all variables and given/known data
    Prove Existence Unique Real Solution to
    ## x^{3} + x^{2} -1 =0 ## between ## x= \frac{2}{3} \text{and} x=1##

    3. The attempt at a solution

    ## x^{2} ( x+1) =1 ##
    I know that the solution is x =0.75488, but this came from some website. How do I find this number without a calculator?
  2. jcsd
  3. Mar 22, 2014 #2
    You don't actually need to find the solution. You just need to know it exists. Think intermediate value theorem.
  4. Mar 23, 2014 #3


    User Avatar
    Science Advisor

    The intermediate value theorem shows that there exist a solution betweem 2/3 and 1. The mean value theorem shows that there is only one.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted