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Math Help - find x values

  1. #1
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    find x values

    y=e^x
    y=4-x^2

    can we solve these equations manually? how can we find the values for x?
    Thank you
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  2. #2
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    If you are looking to find the solution of \displaystyle e^x= 4-x^2 then I suggest using technology, you can find it using pen and paper but this will be a nasty task.
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  3. #3
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    e^(i*pi)'s Avatar
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    No, it can't be solved algebraically because we have an x as the exponent in the first equation and as a base in the second

    e^x = 4-x^2 \implies e^x + x^2 - 4 = 0. Let f(x) = e^x+x^2-4 and the graphs will be equal where they intersect, thus f(x)=0

    Since f(1.5) > 0 \text{  and  } f(1) < 0 the root is between 1 < x < 1.5 (if you were to do this on pen and paper then you'd use an iterative solution converging on x)


    Out of personal interest how would you know this particular system has two real solutions?
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  4. #4
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    Thank you for your reply. But if we see the graphs they intersect near x=1 and x=-2. But Iwant to get the answers in decimal. Is there any other ways to find them in decimals?
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  5. #5
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    Quote Originally Posted by e^(i*pi) View Post
    Out of personal interest how would you know this particular system has two real solutions?
    You can graph them separately, this should tell a story.
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  6. #6
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    Quote Originally Posted by jerad View Post
    Thank you for your reply. But if we see the graphs they intersect near x=1 and x=-2. But Iwant to get the answers in decimal. Is there any other ways to find them in decimals?
    As explained in post #3 you need to look at an iterative method, do you know newton's or the bisection method?
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  7. #7
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    Quote Originally Posted by jerad View Post
    Thank you for your reply. But if we see the graphs they intersect near x=1 and x=-2. But Iwant to get the answers in decimal. Is there any other ways to find them in decimals?
    Yes. Use technology, as was said in post #2. Or use an iterative procedure, as was said in post #3.
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  8. #8
    Super Member TheChaz's Avatar
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    You could use the methods mentioned in post #7.
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  9. #9
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    Quote Originally Posted by TheChaz View Post
    You could use the methods mentioned in post #7.
    Or in post #6?!
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  10. #10
    Super Member TheChaz's Avatar
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    Quote Originally Posted by pickslides View Post
    Or in post #6?!
    This is like one of those "choose your own adventure" novels.
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  11. #11
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    Thank you very much everyone. I solved it
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