问题标题:
用二分法研究方程x3+3x-1=0的近似解x=x0,借助计算器经过若干次运算得下表:运算次数1…456…解的范围(0,0.5)…(0.3125,0.375)(0.3125,0.34375)(0.3125,0.328125)…若精确到0.
问题描述:
用二分法研究方程x3+3x-1=0的近似解x=x0,借助计算器经过若干次运算得下表:
解的范围 | (0,0.5) | … | (0.3125,0.375) | (0.3125,0.34375) | (0.3125,0.328125) | … |
芦金石回答:
根据运算得下表:
运算次数1…456…解的范围(0,0.5)…(0.3125,0.375)(0.3125,0.34375)(0.3125,0.328125)…因为f(0.3125)<0,且f(0.34375>0,
满足f(0.3125)×f(0.34375)<0,
且区间长度:0.34375-0.3125=0.03125<0.1(精度),
∴n=5,x0=0.3,n+x0=5.3.
故答案为:5.3.
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