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           ☆1 equations

[ 1/1 Equation]
    Work: Find the solution of equation x*(1-x)(1-x) = 25(0.8-x)*0.6*0.6*(0.6-x)*(0.6-x) .
    Question type: Equation
    Solution:Original question:
      x (1 x )(1 x ) = 25(
4
5
x ) ×
3
5
×
3
5
(
3
5
x )(
3
5
x )
    Remove the bracket on the left of the equation:
     Left side of the equation = x × 1(1 x ) x x (1 x )
                                             = x × 1 × 1 x × 1 x x x (1 x )
                                             = x × 1 x × 1 x x x (1 x )
                                             = 1 x x × 1 x x x × 1 + x x x
    The equation is transformed into :
     1 x x × 1 x x x × 1 + x x x = 25(
4
5
x ) ×
3
5
×
3
5
(
3
5
x )(
3
5
x )
     Right side of the equation = 9(
4
5
x )(
3
5
x )(
3
5
x )
    The equation is transformed into :
     1 x x × 1 x x x × 1 + x x x = 9(
4
5
x )(
3
5
x )(
3
5
x )
    Remove the bracket on the right of the equation:
     Right side of the equation = 9 ×
4
5
(
3
5
x )(
3
5
x )9 x (
3
5
x )(
3
5
x )
                                               =
36
5
(
3
5
x )(
3
5
x )9 x (
3
5
x )(
3
5
x )
                                               =
36
5
×
3
5
(
3
5
x )
36
5
x (
3
5
x )9 x (
3
5
x )(
3
5
x )
                                               =
108
25
(
3
5
x )
36
5
x (
3
5
x )9 x (
3
5
x )(
3
5
x )
                                               =
108
25
×
3
5
108
25
x
36
5
x (
3
5
x )9 x (
3
5
x )(
3
5
x )
                                               =
324
125
108
25
x
36
5
x (
3
5
x )9 x (
3
5
x )(
3
5
x )
                                               =
324
125
108
25
x
36
5
x ×
3
5
+
36
5
x x 9 x (
3
5
x )
                                               =
324
125
108
25
x
108
25
x +
36
5
x x 9 x (
3
5
x )(
3
5
x )
                                               =
324
125
216
25
x +
36
5
x x 9 x (
3
5
x )(
3
5
x )
                                               =
324
125
216
25
x +
36
5
x x 9 x ×
3
5
(
3
5
x ) + 9 x
                                               =
324
125
216
25
x +
36
5
x x
27
5
x (
3
5
x ) + 9 x x
                                               =
324
125
216
25
x +
36
5
x x
27
5
x ×
3
5
+
27
5
x x
                                               =
324
125
216
25
x +
36
5
x x
81
25
x +
27
5
x x + 9
                                               =
324
125
297
25
x +
36
5
x x +
27
5
x x + 9 x x
                                               =
324
125
297
25
x +
36
5
x x +
27
5
x x + 9 x x
                                               =
324
125
297
25
x +
36
5
x x +
27
5
x x +
27
5
x x
    The equation is transformed into :
     1 x x × 1 x x x × 1 + x x x =
324
125
297
25
x +
36
5
x x +
27
5
x x +
27
5
x x

    
        x=
2
5
    
    There are 1 solution(s).


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