Systems of equations with one inequality and exponents.The equation is this: 8000 &lt; x y 5 &lt; 8100 x y 4 − x y 3 &gt; 5000I have no idea how to solve for the greater then or less then part of the equation. I also have no idea how to solve for exponents and finally if it even can be solved!

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Systems of equations with one inequality and exponents.The equation is this:  8000  &amp;lt;  x      y    5    &amp;lt;  8100  x      y    4    −  x      y    3    &amp;gt;  5000I have no idea how to solve for the greater then or less then part of the equation. I also have no idea how to solve for exponents and finally if it even can be solved!

Govorei9b · Accepted Answer

The system you have is not solvable.Since we don&#039;t know the exact values of   x      y    5   and   x      y    4    −  x      y    3  , let&#039;s put in some values, say   r and   s, and see what happens. We have:                    (1)                    x                  y          5                =        r                                (2)                    x                  y          4                −        x                  y          3                =        s              8000  &amp;lt;  r  &amp;lt;  8100  s  &amp;gt;  5000We know that   y  ≠  0, since otherwise r would equal zero, contradicting the fact that   r  &amp;gt;  8000  &amp;gt;  0. Thus, from (1), we can find                    (3)                    x        =                  r                      y            5                              Substituting (3) into (2) gives  r      y          −      1        −  r      y          −      2        =  swhich we can multiply by       y    2   to get  r  y  −  r  =  s      y    2                      (4)                    0        =        s                  y          2                −        r        y        +        r            I&#039;m not sure if you&#039;re familiar with the quadratic equation, but we can use the discriminant to tell when (4) will have solutions. Specifically, (4) will have (real) solutions when      r    2    −  4  r  s  &amp;gt;  0But, we know that   s  &amp;gt;  5000, so      r    2    −  4  r  s  &amp;lt;      r    2    −  4  r  (  5000  )      r    2    −  4  r  s  &amp;lt;  r  (  r  −  20000  )But, for   8000  &amp;lt;  r  &amp;lt;  8100, the right hand side is always negative, so our discriminant is always less than zero, and we have no real solutions.

Systems of equations with one inequality and exponents. The equation is this: 8000 <

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