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    1.

    x(3x+1)=0

    x=0 or 3x+1=0

    x=0 or 3x= -1

    x=0 or x= -1/3

    2.

    x^2 - 4x=0

    x(x-4)=0

    x=0 or x-4=0

    x=0 or x=4

    3.

    x^2 -8x+12=0

    if you use quadratic formula︰

    x^2 -8x+12=0

    x=[-b+√(b^2-4ac)]/(2a) or [-b-√(b^2-4ac)]/(2a)

    x={ -(-8) + √[(-8)^2-4(1)(12)] }/[2(1)] or x={ -(-8) - √[(-8)^2-4(1)(12)] }/[2(1)]

    x=6 or x=2

    if you use cross method︰

    x^2 -8x+12=0

    x -6

    x -2

    ________

    =-6x-2x=8x

    ∴(x-2)(x-6)=0

    x=6 or x=2

    if you use completing the square︰

    x^2 -8x+12=0

    x^2 -8x= -12

    x^2 -8x +(8/2)^2 -(8/2)^2= -12

    (x-4)^2 = -12+16

    (x-4)^2 = 4

    (x-4)= √4 or -√4

    x=2+4 or -2+4

    x=6 or 2

    4. x^2 -8x+16=0

    if you use quadratic formula︰

    x^2 -8x+16=0

    x=[-b+√(b^2-4ac)]/(2a) or [-b-√(b^2-4ac)]/(2a)

    x={ -(-8) + √[(-8)^2-4(1)(16)] }/[2(1)] or x={ -(-8) - √[(-8)^2-4(1)(16)] }/[2(1)]

    x=4

    if you use cross method︰

    x^2 -8x+16=0

    x -4

    x -4

    ________

    =-4x-4x=8x

    ∴(x-4)(x-4)=0

    x=4

    if you use completing the square︰

    x^2 -8x+16=0

    x^2 -8x= -16

    x^2 -8x +(8/2)^2 -(8/2)^2= -16

    (x-4)^2 = -16+16

    (x-4)^2 = 0

    (x-4)=0

    x=4

    2014-01-15 18:28:56 補充:

    In 3's cross method,

    it should be

    x -6

    + x -2

    ________

    =(-6x)+(-2x)= -8x

    ∴(x-2)(x-6)=0

    x=6 or x=2

    In 4's cross method,

    it should be

    x -4

    + x -4

    ________

    =(-4x)+(-4x)= -8x

    ∴(x-4)(x-4)=0

    x=4

  • Anonymous
    6 years ago

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  • 6 years ago

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    ^__^ 所以我刪去答案並贊助~

    大家努力!

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