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Math Help - what is the unique values of a

  1. #1
    rcs
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    what is the unique values of a

    can anybody please do me a favor on this problem

    what is the unique values of a-unique-sol-n-2.jpg


    Thank you so very much.
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  2. #2
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    Equation 1 + Equation 2:

    \displaystyle (x^2-y^2) + [(x-a)^2+y^2] = 0+0

    \displaystyle x^2 + x^2 - 2ax + a^2 = 0

    \displaystyle 2x^2 - 2ax + a^2 = 0.


    This is a quadratic. For a unique solution, \displaystyle \Delta = 0.

    \displaystyle (-2a)^2 - 4(2)(a^2) = 0

    \displaystyle 4a^2 - 8a^2 = 0

    \displaystyle -4a^2 = 0

    \displaystyle a = 0.

    So this system will have a unique solution when \displaystyle a = 0.
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  3. #3
    rcs
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    so amazing sir Prove it, there is one thing i would like to ask hope you wouldn't mind... how did u get the (-2a)^2 -4(2)(a) = 0 ?

    thanks a lot
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  4. #4
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    Quote Originally Posted by rcs View Post
    so amazing sir Prove it, there is one thing i would like to ask hope you wouldn't mind... how did u get the (-2a)^2 -4(2)(a) = 0 ?

    thanks a lot
    For a quadratic in the form ax^2+bx+c=0 , it has one solution if b^2-4ac=0
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  5. #5
    rcs
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    ahh ic the discriminant.. thank you so so much sir pickslides
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