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Math Help - solve the equation

  1. #1
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    solve the equation

    hi,
    i nned to solve this equation:
    x^3-5x=8

    x=2.7


    im unsure how to work this out.
    i know i would do 2.7^3-13.5x=8 but i don't know what to do after this.

    some help would be great!

    thanks!
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  2. #2
    Senior Member Sambit's Avatar
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    Let f(x)=x^3-5x-8 so that you have to find a value of x that satisfies the equation f(x)=0. Observe that f(2)<0 and f(3)>0. So there lies x , (where 2<x<3,) such that f(x)=0.

    See that f(2.5) < 0. So for f(x) to be 0 , you have 2.5<x<3.

    After this take x=2.6,2.65,... so on and notice when f(x) changes its sign. After afew couple of steps you will get the solution according to what precision you want to maintain.

    However, the correct solution is 2.8025
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  3. #3
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    2.7 is not a solution to the equation you posted. did you type it correctly?

    editincorrect comment removed, oops.
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  4. #4
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    springfan25- yes i have to find if 2.7 works or not and the second part is 2.8 but i was going to do that on my own.
    sambit- i don't really understand what you have written. could i -8 from each side to get 2.7^3-13.5x-8=0 and do a quadratic equation?
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  5. #5
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    This is a cubic equation so no you could not 'do a quadratic equation'. I assume you are doing numerical methods. In which case the bisection method outlined by Sambit could be used.
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  6. #6
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    Quote Originally Posted by poirot View Post
    This is a cubic equation so no you could not 'do a quadratic equation'. I assume you are doing numerical methods. In which case the bisection method outlined by Sambit could be used.
    oh ok, would you care to explain it to me more simple please as i can't understand what sambit has posted.
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  7. #7
    Senior Member Sambit's Avatar
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    Quote Originally Posted by andyboy179 View Post
    sambit- i don't really understand what you have written. could i -8 from each side to get 2.7^3-13.5x-8=0 and do a quadratic equation?
    Quote Originally Posted by andyboy179 View Post
    oh ok, would you care to explain it to me more simple please as i can't understand what sambit has posted.
    To begin with, think in simple way. x=2 and x-2=0 are equivalent. Aren't they? So here solving x^3-5x=8 is equivalent to solving x^3-5x-8=0. Alright? You are just subtracting 8 from both the sides; so they must be equivalent.

    Next try to understand what does a solution of an equation mean. I suppose you have the preliminary concept regarding function and graph. If you are gievn a function f(x) (for example, here you have f(x)=x^3-5x=8), plot f(x) in a graph ( that is, put values of x along horizontal X-axis and values of f(x) along vertical Y-axis). The function will have a solution at x_0 if f(x)is 0 at x=x_0 (that is f(x_0)=0). In this case, your function looks like THIS. The blue line denotes f(x). Notice that as x increases, f(x) increases ( f(x) becomes +ve from -ve). During this increase, the curve cuts the X-axis at some point (red point)-- that particular point is the solution of your equation.

    So this is the concept. This is why you should find two consecutive values of x_1 , x_2 such that f(x_1)<0 and f(x_2)>0, because your required solution always lies in between x_1 and x_2

    Now I hope you'll understand what my previous post meant.

    The red point is the solution: 2.80259
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