用配方法解:3y方+1=2乘根号3y (2)2x方=3-7x (3)6x方-x-2=0 (4)9x方+6x方-8=0

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  • (1)3y方+1=2乘根号3y

    3y方-2乘根号3y =-1

    y^2-2乘三分之根号3/y =-1/3

    y^2-2乘根号3/3y +(三分之根号3)^2=-1/3+(三分之根号3/)^2

    (y-三分之根号3)^2=0

    解得y1=y2=三分之根号3

    (2)2x方=3-7x

    2x^2+7x=3

    x^2+7/2*x=3/2

    x^2+7/2*x+(7/4)^2=3/2+(7/4)^2

    (x+7/4)^2=73/16

    x+7/4=4分之根号73或x+7/4=-4分之根号73

    即x1=4分之根号73-7/4 x2=-4分之根号73-7/4

    (3)6x方-x-2=0

    6x^2-x=2

    x^2-1/6*x=1/3

    x^2-1/6*x+(1/12)^2=1/3+(1/12)^2

    (x-1/12)^2=49/144

    x-1/12=7/12 或 x-1/12=-7/12

    即x1= 2/3 x2=-1/2

    (4)9x方+6x方-8=0

    15x^2=8

    x^2=8/15

    x1= 15分之*陪根号30,x2=-15分之*陪根号30

    (5)5x方-3=x方

    5^2-x^2=3

    4x^2=3

    x^2=3/4

    x1= 2分之根号3 ,x2=-2分之根号3