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Math Help - Simultaneous equation help:

  1. #1
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    Simultaneous equation help:

    4x^2 + y^2 = 25 and xy = 6.

    I made y = 6/ x and got the equation :

    4x^2 +( 6 / x )^2 = 25.

    I thought i could then make it 4x ^ 2 + 36 / x^2 = 25.

    Is that correct so far or completely wrong?
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  2. #2
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    Re: Simultaneous equation help:

    Quote Originally Posted by Mathematix View Post
    4x^2 + y^2 = 25 and xy = 6.

    I made y = 6/ x and got the equation :

    4x^2 +( 6 / x )^2 = 25.

    I thought i could then make it 4x ^ 2 + 36 / x^2 = 25.

    Is that correct so far or completely wrong?
    (2x+y)^2-4xy=25

    (2x+y)^2-24=25 ...etc.
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  3. #3
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    e^(i*pi)'s Avatar
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    Re: Simultaneous equation help:

    Quote Originally Posted by Mathematix View Post
    4x^2 + y^2 = 25 and xy = 6.

    I made y = 6/ x and got the equation :

    4x^2 +( 6 / x )^2 = 25.

    I thought i could then make it 4x ^ 2 + 36 / x^2 = 25.

    Is that correct so far or completely wrong?
    That's correct thus far. As long as x \neq 0 you can multiply through by x^2

    4x^4 + 36 = 25x^2 \Leftrightarrow 4x^4-25x^2+36 = 0 \Leftrightarrow (x^2-4)(4x^2-9) = 0

    Both of those factors can be further factored using the difference of two squares to give x values.

    Don't forget to check for extraneous solutions at the end if you use this method
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  4. #4
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    Re: Simultaneous equation help:

    ^ I got to that point earlier but didn't continue to calculate it, because I thought it was wrong. I understand now, got the correct values for x and y. Thanks!
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