5到奥数题(好的加分)1.已知关于x的方程a(x-3)+b(3x+1)=5(x+1)有无穷多个解,则a=______,b
0
0

3个回答

  • 1.a(x-3)+b(3x+1)=5(x+1),

    ax-3a+3bx+b=5x+5

    (a+3b-5)x=5+3a-b

    x有无穷多个解:a+3b-5=0,5+3a-b=0; 则a=-1,b=2.

    2.若关于x、y的方程组{ax+3y=9 2x-y=1 无解,则a的值为( A.-6)

    2x-y=1; y=2x-1;

    ax+3(2x-1)=9

    (a+6)x = 12,a=-6时无解.

    3.若4x-3y-6z=0,x+2y-7z=0(xyz不等于0),

    7z = x+2y

    6z= 4x-3y

    z=-3x+5y

    7(-3x+5y) = x+2y

    y=(2/3)x; z=(1/3)x

    5x^2+2y^2-z^2 = 5x^2 + (8/9)x^2 - (1/9)x^2 = (52/9)x^2

    2x^2-3y^2-10z^2 = 2x^2 - (12/9)x^2 - (10/9)x^2 = -(4/9)x^2

    5x^2+2y^2-z^2/1x^2-3y^2-10z^2的值等于=(52/9)/(-4/9) = -13; 选D.

    4.题目有误:abc,没有xyz

    ab/(a+b) = 1/3; b= a/(3a-1)

    bc/(b+c) = 1/4; c= b/(4b-1) = {a/(3a-1)}/{4a/(3a-1) -1} = a/(a+1);

    ac/(a+c) = 1/5; c= a/(5a-1)

    则 a/(a+1) = a/(5a-1); a= 1/2;

    b = 1; c = 1/3.

    代入计算即可.

    5.

    2x-3y+4m=11 (1)

    3x+2y+5m=21 (2)

    (1)*2 + (2)*3 :13x + 23m = 85; x= (85-23m)/13;

    (2)*2 - (1)*3 :13y - 2m = 9; y= (9+2m)/13;

    代入x,y:

    x+3y+7m=20

    (85-23m)/13 + 3(9+2m)/13 + 7m =20

    74m=148

    m=2,选C.

更多回答