SOLUTION: Solve 3√x + 5/√ x = 16.

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Question 1186258: Solve 3√x + 5/√ x = 16.
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20855) About Me  (Show Source):
Answer by ikleyn(53751) About Me  (Show Source):
You can put this solution on YOUR website!
.
Solve 3%2Asqrt%28x%29 + 5%2Fsqrt%28x%29 = 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. 


Your starting equation is

    3%2Asqrt%28x%29 + 5%2Fsqrt%28x%29 = 16.


Introduce new variable  y = sqrt%28x%29.  Then the given equation takes the form

    3y + 5%2Fy = 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%2F3.


Hence,  for  x = y%5E2,  we have two values  5%5E2 = 25  and  %281%2F3%29%5E2 = 1%2F9.


ANSWER.  The given equation has two solutions  x= 25  and/or  x= 1%2F9.


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

Solved.