Question

用二分法求方程x+1/x-3=0在区间(2,3)内的近似值

Answer 1

f(x)=x+1/x-3
f(2)=-0.5 f(3)=1/3
f(x)是减函数
x1=2 x2=3
x1 f((x1+x2)/2) x2 (x1+x2)/2
2.0000000000 -0.1000000000 3.0000000000 2.5000000000
x1= (x1+x2)/2
2.5000000000 0.1136363636 3.0000000000 2.7500000000
x2=(x1+x2)/2
2.5000000000 0.0059523810 2.7500000000 2.6250000000
2.5000000000 -0.0472560976 2.6250000000 2.5625000000
2.5625000000 -0.0207078313 2.6250000000 2.5937500000
2.5937500000 -0.0073914671 2.6250000000 2.6093750000
2.6093750000 -0.0007229478 2.6250000000 2.6171875000
2.6171875000 0.0026138692 2.6250000000 2.6210937500
2.6171875000 0.0009452484 2.6210937500 2.6191406250
2.6171875000 0.0001110972 2.6191406250 2.6181640625
2.6171875000 -0.0003059386 2.6181640625 2.6176757813

2.6171875000<x<2.6181640625