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☆1 equations
[ 1/1 Equation]
Work: Find the solution of equation 1/(d+10) = 1/d+1/(d+1)+1/(d+2) .
Question type: Equation
Solution:Original question:| | 1 | ÷ | ( | d | + | 10 | ) | = | 1 | ÷ | d | + | 1 | ÷ | ( | d | + | 1 | ) | + | 1 | ÷ | ( | d | + | 2 | ) |
| Multiply both sides of the equation by: | ( | d | + | 10 | ) | , | d |
| | 1 | d | = | 1 | ( | d | + | 10 | ) | + | 1 | ÷ | ( | d | + | 1 | ) | × | ( | d | + | 10 | ) | d | + | 1 | ÷ | ( | d | + | 2 | ) | × | ( | d | + | 10 | ) | d |
Remove a bracket on the right of the equation:：
| | 1 | d | = | 1 | d | + | 1 | × | 10 | + | 1 | ÷ | ( | d | + | 1 | ) | × | ( | d | + | 10 | ) | d | + | 1 | ÷ | ( | d | + | 2 | ) | × | ( | d | + | 10 | ) | d |
The equation is reduced to :
| | 1 | d | = | 1 | d | + | 10 | + | 1 | ÷ | ( | d | + | 1 | ) | × | ( | d | + | 10 | ) | d | + | 1 | ÷ | ( | d | + | 2 | ) | × | ( | d | + | 10 | ) | d |
| Multiply both sides of the equation by: | ( | d | + | 1 | ) |
| | 1 | d | ( | d | + | 1 | ) | = | 1 | d | ( | d | + | 1 | ) | + | 10 | ( | d | + | 1 | ) | + | 1 | ( | d | + | 10 | ) | d | + | 1 | ÷ | ( | d | + | 2 | ) | × | ( | d | + | 10 | ) | d |
Remove a bracket on the left of the equation:
| | 1 | d | d | + | 1 | d | × | 1 | = | 1 | d | ( | d | + | 1 | ) | + | 10 | ( | d | + | 1 | ) | + | 1 | ( | d | + | 10 | ) | d | + | 1 | ÷ | ( | d | + | 2 | ) | × | ( | d | + | 10 | ) | d |
Remove a bracket on the right of the equation:：
| | 1 | d | d | + | 1 | d | × | 1 | = | 1 | d | d | + | 1 | d | × | 1 | + | 10 | ( | d | + | 1 | ) | + | 1 | ( | d | + | 10 | ) | d | + | 1 |
The equation is reduced to :
| | 1 | d | d | + | 1 | d | = | 1 | d | d | + | 1 | d | + | 10 | ( | d | + | 1 | ) | + | 1 | ( | d | + | 10 | ) | d | + | 1 | ÷ | ( | d | + | 2 | ) |
| Multiply both sides of the equation by: | ( | d | + | 2 | ) |
| | 1 | d | d | ( | d | + | 2 | ) | + | 1 | d | ( | d | + | 2 | ) | = | 1 | d | d | ( | d | + | 2 | ) | + | 1 | d | ( | d | + | 2 | ) | + | 10 | ( | d | + | 1 | ) | ( | d | + | 2 | ) | + | 1 | ( | d | + | 10 | ) |
Remove a bracket on the left of the equation:
| | 1 | d | d | d | + | 1 | d | d | × | 2 | + | 1 | d | ( | d | + | 2 | ) | = | 1 | d | d | ( | d | + | 2 | ) | + | 1 | d | ( | d | + | 2 | ) | + | 10 | ( | d | + | 1 | ) | ( | d | + | 2 | ) | + | 1 | ( | d | + | 10 | ) |
Remove a bracket on the right of the equation:：
| | 1 | d | d | d | + | 1 | d | d | × | 2 | + | 1 | d | ( | d | + | 2 | ) | = | 1 | d | d | d | + | 1 | d | d | × | 2 | + | 1 | d | ( | d | + | 2 | ) | + | 10 |
The equation is reduced to :
| | 1 | d | d | d | + | 2 | d | d | + | 1 | d | ( | d | + | 2 | ) | = | 1 | d | d | d | + | 2 | d | d | + | 1 | d | ( | d | + | 2 | ) | + | 10 | ( | d | + | 1 | ) |
Remove a bracket on the left of the equation:
| | 1 | d | d | d | + | 2 | d | d | + | 1 | d | d | + | 1 | d | = | 1 | d | d | d | + | 2 | d | d | + | 1 | d | ( | d | + | 2 | ) | + | 10 | ( | d | + | 1 | ) |
Remove a bracket on the right of the equation:：
| | 1 | d | d | d | + | 2 | d | d | + | 1 | d | d | + | 1 | d | = | 1 | d | d | d | + | 2 | d | d | + | 1 | d | d | + | 1 | d |
The equation is reduced to :
| | 1 | d | d | d | + | 2 | d | d | + | 1 | d | d | + | 2 | d | = | 1 | d | d | d | + | 2 | d | d | + | 1 | d | d | + | 2 | d |
Remove a bracket on the right of the equation:：
| | 1 | d | d | d | + | 2 | d | d | + | 1 | d | d | + | 2 | d | = | 1 | d | d | d | + | 2 | d | d | + | 1 | d | d | + | 2 | d |
The equation is reduced to :
| | 1 | d | d | d | + | 2 | d | d | + | 1 | d | d | + | 2 | d | = | 1 | d | d | d | + | 2 | d | d | + | 1 | d | d | + | 2 | d |
Remove a bracket on the right of the equation:：
| | 1 | d | d | d | + | 2 | d | d | + | 1 | d | d | + | 2 | d | = | 1 | d | d | d | + | 2 | d | d | + | 1 | d | d | + | 2 | d |
The equation is reduced to :
| | 1 | d | d | d | + | 2 | d | d | + | 1 | d | d | + | 2 | d | = | 1 | d | d | d | + | 2 | d | d | + | 1 | d | d | + | 2 | d |
The equation is reduced to :
| | 1 | d | d | d | + | 2 | d | d | + | 1 | d | d | + | 2 | d | = | 1 | d | d | d | + | 2 | d | d | + | 1 | d | d | + | 22 | d |
Remove a bracket on the right of the equation:：
| | 1 | d | d | d | + | 2 | d | d | + | 1 | d | d | + | 2 | d | = | 1 | d | d | d | + | 2 | d | d | + | 1 | d | d | + | 22 | d |
The equation is reduced to :
| | 1 | d | d | d | + | 2 | d | d | + | 1 | d | d | + | 2 | d | = | 1 | d | d | d | + | 2 | d | d | + | 1 | d | d | + | 22 | d |
The solution of the equation:
d1≈-14.475218 , keep 6 decimal places
d2≈-1.590405 , keep 6 decimal places
d3≈-0.434377 , keep 6 decimal places
There are 3 solution(s).
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