Question 1186258
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Solve {{{3*sqrt(x)}}} + {{{5/sqrt(x)}}} = 16.
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            @MathLover1 solved  ANOTHER  equation,  DIFFERENT  from the given in the post.


            So her solution and her answer have no any relation to the posed problem.


            I came to bring the correct solution.



<pre>
Your starting equation is

    {{{3*sqrt(x)}}} + {{{5/sqrt(x)}}} = 16.


Introduce new variable  y = {{{sqrt(x)}}}.  Then the given equation takes the form

    3y + {{{5/y}}} = 16.


Multiply both sides by y.  You will get an EQUIVALENT equation

    3y^2 + 5 = 16y,  

or

    3y^2 - 16y + 5 = 0.


Apply the quadratic formula and find the roots.   They are  y = 5  and  y = {{{1/3}}}.


Hence,  for  x = {{{y^2}}},  we have two values  {{{5^2}}} = 25  and  {{{(1/3)^2}}} = {{{1/9}}}.


<U>ANSWER</U>.  The given equation has two solutions  x= 25  and/or  x= {{{1/9}}}.


You can easily check it by substituting these found values of x into the original equation.
</pre>

Solved.