Help! (I got a different answer using another way)

  • M0★ M2★ M3★ M4★ M5

    Admins please help!
    When I did Your Turn I used a way where:
    ab+bc+ca = 3+6+8
    2(a+b+c) = 17
    a+b+c = 17/2 = 8.5
    And I got this different answer.
    I totally understand Professor Loh’s way of doing the question, but I don’t get how we could get different answers.
    I am currently trying to check for any silly mistakes.

  • ADMIN M0★ M1 M5

    @RZ923 Hi there! I think I see it. Going from the line

    $$ ab + bc + ca = 3 + 6 + 8$$

    to the line

    $$ 2 \left( a + b + c \right) = 17,$$

    there is the assumption that two \(a's\) are added together, two \(b's\) are added together, and two \(c's\) are added together. In actuality, though, \( ab \neq a + b, bc \neq b + c,\) and \( ca \neq c + a.\)

    Yours is the solution you would use if the question looked instead like this:

    $$\begin{aligned} a + b &= 3 \\ a + c &= 6 \\ b + c &= 8 \\ \end{aligned} $$

    Instead we should actually multiply the \(ab, bc,\) and \(ac\) together, like this:

    $$ (ab)(bc)(ac) = 3 \times 6 \times 8 $$

    which gives us

    $$ a^2 b^2 c^2 = 144 $$
    and we can see rather easily that \(abc = 12.\)

    🙂

  • M0★ M2★ M3★ M4★ M5

    Thanks!
    🙂