求方程2的X次方加上3X=7的近似解
来源:学生作业帮 编辑:搜狗做题网作业帮 分类:数学作业 时间:2024/08/06 14:22:53
求方程2的X次方加上3X=7的近似解
![求方程2的X次方加上3X=7的近似解](/uploads/image/z/19032356-20-6.jpg?t=%E6%B1%82%E6%96%B9%E7%A8%8B2%E7%9A%84X%E6%AC%A1%E6%96%B9%E5%8A%A0%E4%B8%8A3X%3D7%E7%9A%84%E8%BF%91%E4%BC%BC%E8%A7%A3)
f(x)=2^x+3x-7
f(1)=-2
f(2)=3
f(x)在实数域严格单增,故方程f(x)=0有且仅有一个实根,且该根在区间(1,2)上.
利用迭代法:
f(x)=0解得
x=(7-2^x)/3
则迭代式
x(n+1)=[7-2^x(n)]/3
取初值1.5,利用EXCELL表下拉计算得:
1.390524292
1.459420199
1.416673923
1.443435621
1.426774145
1.437183641
1.430694257
1.434745299
1.432218546
1.433795388
1.43281167
1.433425492
1.433042528
1.433281479
1.433132392
1.433225413
1.433167375
1.433203587
1.433180993
1.43319509
1.433186295
1.433191782
1.433188358
1.433190495
1.433189162
1.433189994
1.433189475
1.433189798
1.433189596
1.433189722
1.433189644
1.433189693
1.433189662
1.433189681
1.433189669
1.433189677
1.433189672
1.433189675
1.433189673
1.433189674
1.433189674
1.433189674
1.433189674
1.433189674
1.433189674
可见,近似解为x=1.433189674
精度可达小数点后8位.
f(1)=-2
f(2)=3
f(x)在实数域严格单增,故方程f(x)=0有且仅有一个实根,且该根在区间(1,2)上.
利用迭代法:
f(x)=0解得
x=(7-2^x)/3
则迭代式
x(n+1)=[7-2^x(n)]/3
取初值1.5,利用EXCELL表下拉计算得:
1.390524292
1.459420199
1.416673923
1.443435621
1.426774145
1.437183641
1.430694257
1.434745299
1.432218546
1.433795388
1.43281167
1.433425492
1.433042528
1.433281479
1.433132392
1.433225413
1.433167375
1.433203587
1.433180993
1.43319509
1.433186295
1.433191782
1.433188358
1.433190495
1.433189162
1.433189994
1.433189475
1.433189798
1.433189596
1.433189722
1.433189644
1.433189693
1.433189662
1.433189681
1.433189669
1.433189677
1.433189672
1.433189675
1.433189673
1.433189674
1.433189674
1.433189674
1.433189674
1.433189674
1.433189674
可见,近似解为x=1.433189674
精度可达小数点后8位.
求方程6-3x=2的x次方的近似解(精确到0.1)
没带计算器 求3的X次方=X+4方程的近似解
求方程2(的x次方)+x=4的近似解.
求方程2(x次方)+x=4的近似解.
用二分法求方程X的3次方+5=0的一个近似解
解方程 9的x次方加上6的x次方=2的2x+1次方
用二分法求方程In(2x+6)+2=3的 x次方在区间(1,2)内的近似解(精确到0.1)
C语言 二分法求方程x^2-3x-5=0的近似解
用二分法求方程近似解方程(x+1)(x-2)(x-3)=1在区间(-1,0)的近似解(精确度0.1)
6的x次方加上4的x次方等于9的x次方.解方程.
用二分法求方程x=5减去e的x次方在(1,2)内的近似解 精确到0.1
借助计算器或计算机,用二分法求方程x^3+5=6x^2+3x的近似解