因式分解:12x^2-5x-2;2x^2+4xy+2y^2-8z^2 解方程:{x+y^2=6,y=x};x-12+根号

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  • 12x^2-5x-2=(3x^2-2)*(4x^2+1)

    2x^2+4xy+2y^2-8z^2=2(x+y+2z)*(x+y-2z)

    解方程:{x+y^2=6,y=x};

    y=x

    x+x^2-6=0

    (x+3)*(x-2)=0

    x=-3或x=2

    x-12+根号x=0;

    x=(12-x)^2

    x=144+x^2-24x

    x^2-25x+144=0

    (x-16)*(x-9)=0

    x=16或x=9

    x^2 +3x+根号(x^2+3x)=6

    设x^2+3x=t

    则t+根号t=6

    根号t=6-t

    t=(6-t)^2

    (t-4)*(t-9)=0

    t=4或t=9

    即x^2+3x=4或x^2+3x=9

    x^2+3x=4时

    (x+4)*(x-1)=0

    x=1或x=-4

    x^2+3x=9时

    (x+3/2)^2=27/4

    x=-3/2+3/2*根号3

    或x=-3/2-3/2*根号3