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           ☆1 equations

[ 1/1 Equation]
    Work: Find the solution of equation s(0.5s+1)(0.1s+1)(0.023s+1) = 10(0.23s+1) .
    Question type: Equation
    Solution:Original question:
      s (
1
2
s + 1)(
1
10
s + 1)(
23
1000
s + 1) = 10(
23
100
s + 1)
    Remove the bracket on the left of the equation:
     Left side of the equation = s ×
1
2
s (
1
10
s + 1)(
23
1000
s + 1) + s × 1(
1
10
s + 1)(
23
1000
s + 1)
                                             = s ×
1
2
s ×
1
10
s (
23
1000
s + 1) + s ×
1
2
s × 1(
23
1000
s + 1) + s × 1(
1
10
s + 1)(
23
1000
s + 1)
                                             = s ×
1
20
s s (
23
1000
s + 1) + s ×
1
2
s (
23
1000
s + 1) + s × 1(
1
10
s + 1)(
23
1000
s + 1)
                                             = s ×
1
20
s s ×
23
1000
s + s ×
1
20
s s × 1 + s ×
1
2
s (
23
1000
s + 1) + s × 1(
1
10
s + 1)(
23
1000
s + 1)
                                             = s ×
23
20000
s s s + s ×
1
20
s s + s ×
1
2
s (
23
1000
s + 1) + s × 1(
1
10
s + 1)(
23
1000
s + 1)
                                             = s ×
23
20000
s s s + s ×
1
20
s s + s ×
1
2
s ×
23
1000
s + s ×
1
2
s × 1 + s × 1(
1
10
s + 1)(
23
1000
s + 1)
                                             = s ×
23
20000
s s s + s ×
1
20
s s + s ×
23
2000
s s + s ×
1
2
s + s × 1(
1
10
s + 1)(
23
1000
s + 1)
                                             = s ×
23
20000
s s s + s ×
1
20
s s + s ×
23
2000
s s + s ×
1
2
s + s × 1 ×
1
10
s (
23
1000
s + 1) + s × 1 × 1(
23
1000
s + 1)
                                             = s ×
23
20000
s s s + s ×
1
20
s s + s ×
23
2000
s s + s ×
1
2
s + s ×
1
10
s (
23
1000
s + 1) + s × 1(
23
1000
s + 1)
                                             = s ×
23
20000
s s s + s ×
1
20
s s + s ×
23
2000
s s + s ×
1
2
s + s ×
1
10
s ×
23
1000
s + s ×
1
10
s × 1 + s × 1(
23
1000
s + 1)
                                             = s ×
23
20000
s s s + s ×
1
20
s s + s ×
23
2000
s s + s ×
1
2
s + s ×
23
10000
s s + s ×
1
10
s + s × 1(
23
1000
s + 1)
                                             = s ×
23
20000
s s s + s ×
1
20
s s + s ×
23
2000
s s + s ×
1
2
s + s ×
23
10000
s s + s ×
1
10
s + s × 1 ×
23
1000
s + s × 1 × 1
                                             = s ×
23
20000
s s s + s ×
1
20
s s + s ×
23
2000
s s + s ×
1
2
s + s ×
23
10000
s s + s ×
1
10
s + s ×
23
1000
s + s × 1
    The equation is transformed into :
      s ×
23
20000
s s s + s ×
1
20
s s + s ×
23
2000
s s + s ×
1
2
s + s ×
23
10000
s s + s ×
1
10
s + s ×
23
1000
s + 1 s = 10(
23
100
s + 1)
    Remove the bracket on the right of the equation:
     Right side of the equation = 10 ×
23
100
s + 10 × 1
                                               =
23
10
s + 10
    The equation is transformed into :
      s ×
23
20000
s s s + s ×
1
20
s s + s ×
23
2000
s s + s ×
1
2
s + s ×
23
10000
s s + s ×
1
10
s + s ×
23
1000
s + 1 s =
23
10
s + 10

    The solution of the equation:
        s1≈-42.083767 , keep 6 decimal places
        s2≈-13.904485 , keep 6 decimal places
        s3≈-3.608357 , keep 6 decimal places
        s4≈4.118348 , keep 6 decimal places
    
    There are 4 solution(s).


解程的详细方法请参阅:《方程的解法》



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