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Math Help - Equivalent Quadratics.

  1. #1
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    Equivalent Quadratics.

    I understand that these equations are equivalent but I do not understand how. Please show me how you manipulate the original equation to get the other equations. Help Thanks.

    Original Equation: x^4-13x^2+36=0

    (2x^2)-2(2x^2)13+144=0

    (2x^2)^2-2(2x^2)13+169=25
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: Equivalent Quadratics.

    Work it out, for example the first one:
    (2x)^2-2(2x^2)13+144=0
    4x^2-4x^2\cdot 13+144=0
    Dividing the ride and left side by 4 gives:
    x^2-13x^2+36=0
    which is the given equation.

    For the other, put 25 from the right side to the left side and so: 169-25=144, which is equivalent to the other two equations.
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  3. #3
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    Re: Equivalent Quadratics.

    Hello, theloser!

    I understand that these equations are equivalent, but I do not understand how.
    Please show me how you manipulate the original equation to get the other equation.

    Original Equation: x^4-13x^2+36\:=\:0

    (2x^2)^2-2(2x^2)13+169=25

    We are given: . . . . x^4 - 12x^2 + 36 \:=\:0

    Multiply by 4: . . . 4x^4 - 52x^2 + 144 \:=\:0

    . . . . . (2x^2)(2x^2) - 2\!\cdot\!2\!\cdot\!13\!\cdot\!x^2 + 144 \:=\:0

    . . . . . . . (2x^2)^2 - 2(2x^2)(13) + 144 \:=\:0

    Add 25: . (2x^2)^2 - 2(2x^2)(13) + 169 \:=\:25


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  4. #4
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    Re: Equivalent Quadratics.

    I didn't even see that. Thanks.
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