六年级解方程练习题。

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WOLFRAM LANGUAGE HOW TO
How to | Solve an Equation
The Wolfram Language has many powerful features that enable you to solve many kinds of equations.
You can solve an equation using . Remember to use &==& in an equation, not just &=&:
The result is a
inside a doubly nested list. The outer list holds all of the solutions and each inner list holds a single solution. Here there are three solutions:
To solve a system of equations, use a list in the first argument:
Here there are two solutions to a simultaneous each solution set is wrapped in its own list:
Here the solution expresses one variable in terms of another:
To use one of these solutions (here the first one is shown), use
(the short form of ) to extract it from the list of solutions and use
(the short form of ) to apply the rule:
For example, here is a plot of
for different values of , assuming that the first solution holds:
In a system of equations with multiple variables, you can solve for some or all of the variables by using a list in the second argument:
If the system is underspecified, the Wolfram Language will give an answer in terms of the remaining variables:
finds what are known as &generic& solutions to equations. These are solutions that do not depend on the variables not specified in the second argument. For example:
No matter what
is, putting in 0 for
solves the equation. But there is another solution that does depend on : namely, setting
to 0. Adding
in the second argument makes this solution show up:
There are other cases in which
does not find every solution. For example:
You can also solve radical equations:
Note that in radical equations,
discards parasite solutions. To see all candidate solutions, including parasites, set the
option to :
This checks the solutions:
You can also solve equations by using :
The output of
is different from the output of :
outputs a logical expression that is equivalent to the original equation, so it never omits a solution:
The Wolfram Language also allows you to get numeric solutions for equations.
For example, you can use
on the output of
to get a numeric approximation for the symbolic solution:
You can also get the numeric solution directly by using , which is faster than combining
to solve a more complicated polynomial equation:
You can also use
to solve systems of equations numerically. Use the same syntax as you would with :
If your equations involve only linear functions or polynomials, then you can use
to get numerical approximations to all the solutions. However, when your equations involve more complicated functions, there is, in general, no systematic procedure for finding all solutions, even numerically. In such cases, you can use
to search for solutions.
to search for numerical solutions for , starting at 1:
       
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Enable JavaScript to interact with content and submit forms on Wolfram websites.在线解方程_数学计算_科学计算_工程计算出图像
如图1&x&2时能使f(x)=g(x)
而当1&x&2则g(x)=1
则f(x)=1,
则有唯一解x=(4/3)^(1/3)
【注】本题作图法解题虽然很直观方便但不是很严谨,但要给出严谨的证明又过于复杂所以考虑之下还是给出直观解比较好。
另外如果要严谨证明可做如下尝试。
x-1&[x]≤x
3x^3-[x]=3,
x-1&3x^3-3=[x]≤x
3x^3-3-(x-1)&0① 且3x^3-3≤x②
解出两个不等式确定x的范围在求出g(x)值带入f(x)=g(x)的等式中即可求出x的值,也就是说我用图像法代替了严格确定x的范围这步,其后的步骤一样。
您的举报已经提交成功,我们将尽快处理,谢谢!
易知x&0,x=[x]+{x}→ [x]=x-{x}.
∴x^3-x=3-{x}.
而0≤{x}&1,故
{x(x^2-1)≤3,
{x(x^2-1&2...
配方法,从最高次幂开始凑出带有(x+3)的代数式
题目写错了吧,应该是能被(x-3)除吧
=x^3-3x^2+3x^2-10x+3
...
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