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  • Algebric problem

    From Richard Hachel@21:1/5 to All on Wed Jun 26 14:17:50 2024
    One commenter posed the problem:

    sqrt(3x+7)+sqrt(x+2)=1

    On the French forum, mathematicians had some problems with this.

    However, the solution is very simple, and requires three lines of
    calculations on a piece of paper.

    R.H.

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  • From Jim Burns@21:1/5 to Richard Hachel on Wed Jun 26 11:30:04 2024
    On 6/26/2024 10:17 AM, Richard Hachel wrote:

    One commenter posed the problem:

    sqrt(3x+7)+sqrt(x+2)=1

    On the French forum,
    mathematicians had some problems with this.

    However,
    the solution is very simple,
    and requires three lines of calculations
    on a piece of paper.

    Is the problem that
    some of the possible solutions presented by
    three lines of calculations
    do not produce equality in the original equation?

    Squaring can introduce more possible solutions.

    for each x such that √(3x+7)+√(x+2)=1
    also √(3x+7)=1-√(x+2)

    for each x such that √(3x+7)=1-√(x+2)
    also 3x+7=1-2√(x+2)+x+2
    but also
    for each x such that -√(3x+7)=1-√(x+2)
    also 3x+7=1-2√(x+2)+x+2

    for each x such that
    √(3x+7)=1-√(x+2) or
    -√(3x+7)=1-√(x+2)
    also
    3x+7=1-2√(x+2)+x+2 and
    x+2=-√(x+2)

    for each x such that
    √(3x+7)=1-√(x+2) or
    -√(3x+7)=1-√(x+2) or
    x+2=-√(x+2) or
    x+2=√(x+2)
    also
    (x+2)²=x+2
    (x+1)(x+2)=0
    x=-1 or x=-2

    Only -1 and -2 _can be_ a solution.

    √(3⋅-1+7)+√(-1+2)=√4+√1≠1

    √(3⋅-2+7)+√(-2+2)=√1+√0=1

    Only -2 _is_ a solution.







    R.H.

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  • From Mike Terry@21:1/5 to Richard Hachel on Wed Jun 26 16:19:12 2024
    On 26/06/2024 15:17, Richard Hachel wrote:
    One commenter posed the problem:

    sqrt(3x+7)+sqrt(x+2)=1

    On the French forum, mathematicians had some problems with this.

    However, the solution is very simple, and requires three lines of calculations on a piece of paper.

    R.H.

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    Square both sides + rearrange giving
    ..linear fn of x.. = sqrt(..quadratic fn of x..)
    Square both sides giving
    ..quadratic fn of x.. = ..another quadratic fn of x..
    Solve quadratic giving 2 possibilities for x.
    Check back with original equation (since squaring may introduce extra solutions)

    My working gives the quadratic x^2+3x+2 = 0 solutions x = -1 or x = -2. Checking with original equation: x=-1 fails. x=-2 works, so only solution is x=-2.

    Mike.

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  • From Python@21:1/5 to All on Wed Jun 26 18:21:16 2024
    Le 26/06/2024 à 16:17, Richard Hachel a écrit :
    One commenter posed the problem:

    sqrt(3x+7)+sqrt(x+2)=1

    On the French forum, mathematicians had some problems with this.

    No "mathematician", and almost none of the group usual participants
    has any issues. Only the initial poster (obviously), *you* (making
    a lot of silly mistakes and comments) and Jacques Lavau (as usual)
    had issues.

    However, the solution is very simple, and requires three lines of calculations on a piece of paper.

    Why are you lying and making a fool of yourself in such an idiotic
    way, M.D. Richard "Hachel" Lengrand?

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  • From Richard Hachel@21:1/5 to All on Wed Jun 26 17:06:07 2024
    Le 26/06/2024 à 18:21, Python a écrit :
    Le 26/06/2024 à 16:17, Richard Hachel a écrit :
    One commenter posed the problem:

    sqrt(3x+7)+sqrt(x+2)=1

    However, the solution is very simple, and requires three lines of
    calculations on a piece of paper.

    Why are you lying ?

    Because I like to lie.

    To lie is so wonderfull, so orgasmic.

    Tu devrais essayer, si tu savais comme c'est bon.

    R.H.

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