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On line Solution of Monovariate Equation：
Input any unary equation directly, and then click the "Next" button to obtain the solution of the equation.
It supports equations that contain mathematical functions.
Input any unary equation directly, and then click the "Next" button to obtain the solution of the equation.
It supports equations that contain mathematical functions.
Current location：Equations > Monovariate Equation > The history of univariate equation calculation > Answer
Overview: 1 questions will be solved this time.Among them
☆1 equations
[ 1/1 Equation]
Work: Find the solution of equation 1 = x/（0.24-x）（7.52-x/2）（82.4-x/2） .
Question type: Equation
Solution:Original question:
| 1 | = | x | ÷ | ( | 6 25 | − | x | ) | × | ( | 188 25 | − | x | ÷ | 2 | ) | ( | 412 5 | − | x | ÷ | 2 | ) |
| Multiply both sides of the equation by: | ( | 6 25 | − | x | ) |
| 1 | ( | 6 25 | − | x | ) | = | x | ( | 188 25 | − | x | ÷ | 2 | ) | ( | 412 5 | − | x | ÷ | 2 | ) |
| 1 | × | 6 25 | − | 1 | x | = | x | ( | 188 25 | − | x | ÷ | 2 | ) | ( | 412 5 | − | x | ÷ | 2 | ) |
| 1 | × | 6 25 | − | 1 | x | = | x | × | 188 25 | ( | 412 5 | − | x | ÷ | 2 | ) | − | x | x | ÷ | 2 | × | ( | 412 5 | − | x | ÷ | 2 | ) |
6 25 | − | 1 | x | = | x | × | 188 25 | ( | 412 5 | − | x | ÷ | 2 | ) | − | x | x | × | 1 2 | ( | 412 5 | − | x | ÷ | 2 | ) |
6 25 | − | 1 | x | = | x | × | 188 25 | × | 412 5 | − | x | × | 188 25 | x | ÷ | 2 | − | x | x | × | 1 2 | ( | 412 5 | − | x | ÷ | 2 | ) |
6 25 | − | 1 | x | = | x | × | 77456 125 | − | x | × | 94 25 | x | − | x | x | × | 1 2 | ( | 412 5 | − | x | ÷ | 2 | ) |
6 25 | − | 1 | x | = | 77456 125 | x | − | x | × | 94 25 | x | − | x | x | × | 1 2 | × | 412 5 | + | x | x | × | 1 2 |
6 25 | − | 1 | x | = | 77456 125 | x | − | x | × | 94 25 | x | − | x | x | × | 206 5 | + | x | x | × | 1 4 | x |
After the equation is converted into a general formula, there is a common factor:
( x - 0 )
From
x - 0 = 0
it is concluded that:：
x1=0, it is the incremental root of the eqution.
Solutions that cannot be obtained by factorization:
x2≈15.066289 , keep 6 decimal places
x3≈164.773325 , keep 6 decimal places
There are 3 solution(s).
There is(are) 1 additive root(s) and 2 real solutions.(Note:additive root, generated by computer, but not suitable for this equation.)
解程的详细方法请参阅：《方程的解法》