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Current location：Mathematical operation > History of Mathematical Computation > Answer
Overview: 1 questions will be solved this time.Among them
☆1 equations
[ 1/1 Equation]
Work: Find the solution of equation 198.51/3%［1－1/(1+3%)n］ = 0 .
Question type: Equation
Solution:Original question:
19851 100 | ÷ | 3 100 | × | ( | 1 | − | 1 | ÷ | ( | 1 | + | 3 100 | ) | × | n | ) | = | 0 |
19851 100 | ÷ | 3 100 | × | 1 | − | 19851 100 | ÷ | 3 100 | × | 1 | ÷ | ( | 1 | + | 3 100 | ) | × | n | = | 0 |
| 6617 | − | 6617 | ÷ | ( | 1 | + | 3 100 | ) | × | n | = | 0 |
| Multiply both sides of the equation by: | ( | 1 | + | 3 100 | ) |
| 6617 | ( | 1 | + | 3 100 | ) | − | 6617 | n | = | 0 |
| 6617 | × | 1 | + | 6617 | × | 3 100 | − | 6617 | n | = | 0 |
| 6617 | + | 19851 100 | − | 6617 | n | = | 0 |
681551 100 | − | 6617 | n | = | 0 |
Transposition :
| - | 6617 | n | = | 0 | − | 681551 100 |
Combine the items on the right of the equation:
| - | 6617 | n | = | - | 681551 100 |
By shifting the terms and changing the symbols on toth sides of the equation, we obtain :
681551 100 | = | 6617 | n |
If the left side of the equation is equal to the right side, then the right side must also be equal to the left side, that is :
| 6617 | n | = | 681551 100 |
The coefficient of the unknown number is reduced to 1 :
| n | = | 681551 100 | ÷ | 6617 |
| = | 681551 100 | × | 1 6617 |
| = | 52427 100 | × | 1 509 |
We obtained :
| n | = | 52427 50900 |
Convert the result to decimal form :
| n | = | 1.03 |