Complex Simultaneous Equations

          Welcome back to my blog. I hope you find this blog interesting. Today's blog post would be short and simple as I would be solving only one math question. I got this question from a friend of mine. The question is on simultaneous equations. I know some people know about this concept already but the question I'm about to solve is a very rare type of simultaneous equation question and I had to think a little to figure out the solution. Let's get back to it. 

       

         Find the values of x and y from the equations below:

      X^1/3 + y^1/3 = 6 -----------(i)

     x + y = 72 ----------------(ii)

    To solve this type of question, you'll have to think of a way to get rid of those exponents in equation (i). One easy way to do that is to introduce a common logarithm or natural logarithm to each term in the equation. I will use natural logarithm for this question like this:

    Then using laws of logarithm for exponents, the exponents would become the coefficient of the logarithm. 

      From here, you can solve the simultaneous equation using the substitution method. Here is a picture of the solution below: 

           After solving the question, you should get two x and y values. The graph below will give you an idea of the solution to the simultaneous equation. 

                  Graph of simultaneous equations: blue line represents equation (i) and the green line represents equation (ii)

    

    

  Check:  If you try to plugin the x-values and y-values into the equations, you should get an approximation of the values on the right-hand side of each equation as in the picture below:

             And that is the end of this blog. This question is just like any other simultaneous equation but you just have to do some simplifications to make it look normal. Also, notice that the answers to the question are not whole numbers. That's why you have to approximate to get the same values as in the picture above when checking your answers. I hope you enjoy reading this post. Thank you for your time.

P.S: Pardon me for the low-quality pictures😊😊. I'll improve them next time.

          

    

                  Sources

1.  Solving Simultaneous Equations: The Substitution Method and the Addition Method: Algebra Reference: Electronics Textbook. (n.d.). Retrieved December 09, 2020, from https://www.allaboutcircuits.com/textbook/reference/chpt-4/solving-simultaneous-equations/

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