如图所示,P1(X1,X2),P2(X2,Y2),.PN(XN,YN)在函数Y=9/x(x>0)的图像上,三角形OP1A

1个回答

  • 作P1⊥X轴于D1,P2⊥X轴于D2……Pn⊥X轴于Dn,

    则有x1=y1,x2=y2,……xn=yn;

    x1=y1,x1*y1=9==>x1=y1=3==>OA1=2x1=6

    ==>(A2D2+OA1)*P2D2=9

    (x2+6)*y2=9,x2=y2

    (x2+6)*x2=9==>x2^2+6x2-9=0-->x2=-3+3√2(负值已舍去)

    -->A1A2=2x2=-6+6√2;

    ==>(A3D3+OA2)*P3D3=9

    (x3+6-6+6√2)*y3=9,x3=y3==>(x3+6-6+6√2)*x3=9

    -->x3^2+(6√2)x3-9=0==>x3=-3√2+3√3(负值已舍去)

    -->A2A3=2x3=-6√2+6√3;

    ==>(A4D4+OA3)*P4D4=9

    (x4+6-6+6√2-6√2+6√3)y4=9,x4=y4

    ==>(x4+6√3)x4=9==>x4=-3√3+6=-3√3+3√4(负值已舍去)

    -->A3A4=2x4=-6√3+6√4

    …………

    -->A(n-2)A(n-1)=-6√(n-2)+6√(n-1)

    x(n-1)=y(n-1)=[A(n-2)A(n-1)]/2=-3√(n-2)+3√(n-1);

    ==>A(n-1)An=-6√(n-1)+6√n

    -->xn=yn=[A(n-1)An]/2=-3√(n-1)+3√n

    :

    y1+y2+y3+y4+……+y(n-1)+yn

    =3+(-3+3√2)+(-3√2+3√3)+(-3√3+3√4)+……+[-3√(n-2)+3√(n-1)]+[-3√(n-1)+3√n]

    =3√n