如图,P1(x1,y1),P2(x2,y2),Pn(xn,yn),…在函数y=4/x的图象上,△P1OA1,△P2A1A2,△P3A2A3,△PnAn-1An,都是等腰直角三角形,斜边OA1,A1A2,A2A3...An-1An都在x轴上(1)求P1的坐标(2)求y1+y2+y3+...+y10的值
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![如图,P1(x1,y1),P2(x2,y2),Pn(xn,yn),…在函数y=4/x的图象上,△P1OA1,△P2A1A2,△P3A2A3,△PnAn-1An,都是等腰直角三角形,斜边OA1,A1A2,A2A3...An-1An都在x轴上(1)求P1的坐标(2)求y1+y2+y3+...+y10的值](/uploads/image/z/6792039-63-9.jpg?t=%E5%A6%82%E5%9B%BE%2CP1%EF%BC%88x1%2Cy1%EF%BC%89%2CP2%EF%BC%88x2%2Cy2%EF%BC%89%2CPn%EF%BC%88xn%2Cyn%EF%BC%89%2C%E2%80%A6%E5%9C%A8%E5%87%BD%E6%95%B0y%3D4%2Fx%E7%9A%84%E5%9B%BE%E8%B1%A1%E4%B8%8A%2C%E2%96%B3P1OA1%2C%E2%96%B3P2A1A2%2C%E2%96%B3P3A2A3%2C%E2%96%B3PnAn-1An%2C%E9%83%BD%E6%98%AF%E7%AD%89%E8%85%B0%E7%9B%B4%E8%A7%92%E4%B8%89%E8%A7%92%E5%BD%A2%2C%E6%96%9C%E8%BE%B9OA1%2CA1A2%2CA2A3...An-1An%E9%83%BD%E5%9C%A8x%E8%BD%B4%E4%B8%8A%EF%BC%881%EF%BC%89%E6%B1%82P1%E7%9A%84%E5%9D%90%E6%A0%87%EF%BC%882%EF%BC%89%E6%B1%82y1%2By2%2By3%2B...%2By10%E7%9A%84%E5%80%BC)
如图,P1(x1,y1),P2(x2,y2),Pn(xn,yn),…在函数y=4/x的图象上,△P1OA1,△P2A1A2,△P3A2A3,△PnAn-1An,都是等腰直角三角形,斜边OA1,A1A2,A2A3...An-1An都在x轴上(1)求P1的坐标(2)求y1+y2+y3+...+y10的值
如图,P1(x1,y1),P2(x2,y2),Pn(xn,yn),…在函数y=4/x的图象上,△P1OA1,△P2A1A2,△P3A2A3,△PnAn-1An,都是等腰直角三角形,斜边OA1,A1A2,A2A3...An-1An都在x轴上(1)求P1的坐标(2)求y1+y2+y3+...+y10的值
如图,P1(x1,y1),P2(x2,y2),Pn(xn,yn),…在函数y=4/x的图象上,△P1OA1,△P2A1A2,△P3A2A3,△PnAn-1An,都是等腰直角三角形,斜边OA1,A1A2,A2A3...An-1An都在x轴上(1)求P1的坐标(2)求y1+y2+y3+...+y10的值
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
错了,笨蛋