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Thread: How can I prove that a + b = c = 0?

  1. #1

    How can I prove that a + b = c = 0?

    Hi. I've got an exercise and it says:

    Rational numbers a, b, c satisfy the equation
    (a + b +c)(a + b - c) = c2
    Prove that a + b + c = 0

    I don't know how to prove this. I overall don't know how to prove any equations in math. Can you help me with that?

  2. #2
    Elite Member
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    Quote Originally Posted by Ayylien64 View Post
    Hi. I've got an exercise and it says:

    Rational numbers a, b, c satisfy the equation
    (a + b +c)(a + b - c) = c2
    Prove that a + b + c = 0

    I don't know how to prove this. I overall don't know how to prove any equations in math. Can you help me with that?
    What are your thoughts?

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  3. #3
    Elite Member
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    Quote Originally Posted by Ayylien64 View Post
    Rational numbers a, b, c satisfy the equation
    (a + b +c)(a + b - c) = c2
    Prove that a + b + c = 0
    Do you know that [tex](x+y)(x-y)=x^2-y^2~?[/tex] Do you know the value of [tex]x[/tex] if [tex]x^2=0~?[/tex]
    “A professor is someone who talks in someone else’s sleep”
    W.H. Auden

  4. #4
    Elite Member
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    Quote Originally Posted by Denis View Post
    u = a + b
    (u + c)(u - c) = c^2
    u^2 - c^2 = c^2
    2c^2 = u^2
    c = u / SQRT(2)
    Right. Note a,b, & c are rational numbers.
    “A professor is someone who talks in someone else’s sleep”
    W.H. Auden

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