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Work: Find the solution of equation (100-2a)(50-2a) = 4704 .
Question type: Equation
Solution:Original question:| | ( | 100 | − | 2 | a | ) | ( | 50 | − | 2 | a | ) | = | 4704 |
Remove the bracket on the left of the equation:
| Left side of the equation = | 100 | ( | 50 | − | 2 | a | ) | − | 2 | a | ( | 50 | − | 2 | a | ) |
| = | 100 | × | 50 | − | 100 | × | 2 | a | − | 2 | a | ( | 50 | − | 2 | a | ) |
| = | 5000 | − | 200 | a | − | 2 | a | ( | 50 | − | 2 | a | ) |
| = | 5000 | − | 200 | a | − | 2 | a | × | 50 | + | 2 | a | × | 2 | a |
| = | 5000 | − | 200 | a | − | 100 | a | + | 4 | a | a |
The equation is transformed into :
| | 5000 | − | 300 | a | + | 4 | a | a | = | 4704 |
After the equation is converted into a general formula, it is converted into:
( a - 1 )( a - 74 )=0
From
a - 1 = 0
a - 74 = 0
it is concluded that:：
a1=1
a2=74
There are 2 solution(s).
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