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    I've been set this homework on algebraic proof but am unsure if I'm doing it right. Would I need to write a statement to prove:
    (n+4)^2 - (3n+4) = (n+1)(n+4)+8 ?
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    (Original post by molly_123c)
    I've been set this homework on algebraic proof but am unsure if I'm doing it right. Would I need to write a statement to prove:
    (n+4)^2 - (3n+4) = (n+1)(n+4)+8 ?
    You'd need to write the proposition statement to start, if that's what you mean
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    (Original post by h3rmit)
    You'd need to write the proposition statement to start, if that's what you mean
    So what would I say at the start?
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    Something like" Proposition:  (n+4)^2 - (3n+4) = (n+1)(n+4)+8, also maybe with f(x)=(n+4)^2 - (3n+4) and g(x)=(n+1)(n+4)+8 "

    Then prove it by induction
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    (Original post by h3rmit)
    Something like" Proposition:  (n+4)^2 - (3n+4) = (n+1)(n+4)+8, also maybe with f(x)=(n+4)^2 - (3n+4) and g(x)=(n+1)(n+4)+8 "

    Then prove it by induction
    Okay thank you, I'll do that
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    You should also probably say where  n \in \mathbb{N}
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    (Original post by molly_123c)
    I've been set this homework on algebraic proof but am unsure if I'm doing it right. Would I need to write a statement to prove:
    (n+4)^2 - (3n+4) = (n+1)(n+4)+8 ?
    All you need to do is expand the LHS and manipulate it enough to get the RHS.

    (Original post by h3rmit)
    Something like" Proposition:  (n+4)^2 - (3n+4) = (n+1)(n+4)+8, also maybe with f(x)=(n+4)^2 - (3n+4) and g(x)=(n+1)(n+4)+8 "

    Then prove it by induction
    (Original post by h3rmit)
    You should also probably say where  n \in \mathbb{N}
    Functions of x without any variables of x in them?? Also this statement is true \forall n \in \mathbb{R} not just the set \mathbb{N}

    Furthermore, this is GCSE level. Proof by induction is not covered at this level.

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    (Original post by RDKGames)
    All you need to do is expand the LHS and manipulate it enough to get the RHS.





    Functions of x without any variables of x in them?? Also this statement is true \forall n \in \mathbb{R} not just the set \mathbb{N}

    Furthermore, this is GCSE level. Proof by induction is not covered at this level.

    Lol, I'm just to writing f(x) and g(x).
    In the course notes I've seen, it always specifies natural numbers in the completion step, so that's kind of my default

    I remember a question like this at GCSE but I didn't answer it. How do you prove it without induction?
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    My bad for not seeing this was in the GCSE's section, but OP, why didn't you say anything if you don't use proof by induction?
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    (Original post by h3rmit)
    Lol, I'm just to writing f(x) and g(x).
    In the course notes I've seen, it always specifies natural numbers in the completion step, so that's kind of my default

    I remember a question like this at GCSE but I didn't answer it. How do you prove it without induction?
    Induction is not needed whatsoever.

    As I told OP, you simply expand the LHS and manipulate it to get the RHS.

    A key step many might find tricky to think of is to split the constant once you achieve the form n^2+bn+c on the LHS.
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    (Original post by RDKGames)
    Induction is not needed whatsoever.

    As I told OP, you simply expand the LHS and manipulate it to get the RHS.

    A key step many might find tricky to think of is to split the constant once you achieve the form n^2+bn+c on the LHS.
    Okay, thank you I'll try that: so am I just trying to make it quadratic and then solve it from that form?
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    (Original post by molly_123c)
    Okay, thank you I'll try that: so am I just trying to make it quadratic and then solve it from that form?
    Yes get an expanded quadratic then try to achieve the answer from there onwards by noticing that the answer want a (n+1)(n+4) in your answer, and that expands to n^2+5n+4 meaning thats what you want a part of your manipulated quadratic to be.
 
 
 
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