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On line Solution of Monovariate Equation：
    Input any unary equation directly, and then click the "Next" button to obtain the solution of the equation.
    It supports equations that contain mathematical functions.
    Current location：Equations > Monovariate Equation > The history of univariate equation calculation > Answer

    Overview: 1 questions will be solved this time.Among them
           ☆1 equations

[ 1/1 Equation]
    Work: Find the solution of equation 4 = （4÷3k）（4÷3k）+（3-4÷3k×k）（3-4÷3k×k） .
    Question type: Equation
    Solution:Original question:
     4 = (4 ÷ 3 × k )(4 ÷ 3 × k ) + (3 − 4 ÷ 3 × k k )(3 − 4 ÷ 3 × k k )
    Remove the bracket on the right of the equation:
     Right side of the equation = 4 ÷ 3 × k (4 ÷ 3 × k ) + (3 − 4 ÷ 3 × k k )(3 − 4 ÷ 3 × k k )
                                               =
4
3
 k (4 ÷ 3 × k ) + (3 − 4 ÷ 3 × k k )(3 − 4 ÷ 3 × k k )
                                               =
4
3
 k × 4 ÷ 3 × k + (3 − 4 ÷ 3 × k k )(3 − 4 ÷ 3 × k k )
                                               =
16
9
 k k + (3 − 4 ÷ 3 × k k )(3 − 4 ÷ 3 × k k )
                                               =
16
9
 k k + 3(3 − 4 ÷ 3 × k k ) − 4 ÷ 3 × k k (3 − 4 ÷ 3 × k k )
                                               =
16
9
 k k + 3(3 − 4 ÷ 3 × k k ) −
4
3
 k k (3 − 4 ÷ 3 × k k )
                                               =
16
9
 k k + 3 × 3 − 3 × 4 ÷ 3 × k k −
4
3
 k
                                               =
16
9
 k k + 9 − 4 k k −
4
3
 k k (3 − 4 ÷ 3 × k k )
                                               =
16
9
 k k + 9 − 4 k k −
4
3
 k k × 3 +
4
3
                                               =
16
9
 k k + 9 − 4 k k − 4 k k +
16
9
 k
    The equation is transformed into :
     4 =
16
9
 k k + 9 − 4 k k − 4 k k +
16
9
 k

    After the equation is converted into a general formula, it is converted into:
    ( 2k + 3 )( 2k +√5 )( 2k - √5 )( 2k - 3 )=0
    From
        2k + 3 = 0
        2k +√5 = 0
        2k - √5 = 0
        2k - 3 = 0
    it is concluded that:：
        k1=-
3
2
        k2=-
√5
2
        k3=
√5
2
        k4=
3
2
    
    There are 4 solution(s).

解程的详细方法请参阅：《方程的解法》


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