Solve the System...2

Discussion in 'Other Pre-University Math' started by nycmathguy, Feb 6, 2022.

  1. nycmathguy

    nycmathguy

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    David Cohen questions just for fun.
    Enjoy.

    IMG_20220205_215318.jpg
     
    nycmathguy, Feb 6, 2022
    #1
  2. nycmathguy

    MathLover1

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    sqrt(2)x -sqrt(3)y=sqrt(3)..........1)
    sqrt(3)x -sqrt(8)y=sqrt(2)............2)
    __________________________

    sqrt(2)x -sqrt(3)y=sqrt(3)..........1), solve for y

    sqrt(2)x -sqrt(3)=sqrt(3)y

    sqrt(2)x/sqrt(3) -sqrt(3)/sqrt(3)=y

    sqrt(2)x/sqrt(3) -1=y

    y=(sqrt(2)/sqrt(3))*x -1...............1a)

    go to

    sqrt(3)x -sqrt(8)y=sqrt(2)............2), substitute y

    sqrt(3)x -2sqrt(2)((sqrt(2)/sqrt(3))*x -1)=sqrt(2)........ solve for x

    sqrt(3)x -(2sqrt(2)sqrt(2)/sqrt(3)))x =sqrt(2)-2sqrt(2)

    sqrt(3)x -(4/sqrt(3)))x =-sqrt(2)

    (sqrt(3) -4/sqrt(3))x =-sqrt(2)

    (-sqrt(3)/3)x =-sqrt(2)

    x =-sqrt(2)/(-sqrt(3)/3)

    x =sqrt(6)

    go to

    y=(sqrt(2)/sqrt(3))*x -1...............1a), substitute x

    y=(sqrt(2)/sqrt(3))*sqrt(6) -1

    y=2-1

    y=1
     
    MathLover1, Feb 6, 2022
    #2
    nycmathguy likes this.
  3. nycmathguy

    nycmathguy

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    The David Cohen textbook is pretty cool, right?

    How about this one?

    Difference Quotient
     
    nycmathguy, Feb 6, 2022
    #3
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