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)   (Show Source): You can put this solution on YOUR website!
Answer by ikleyn(53751)   (Show Source): You can put this solution on YOUR website!
.
Solve + = 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

     +  = 16.


Introduce new variable  y = .  Then the given equation takes the form

    3y +  = 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 = .


Hence,  for  x = ,  we have two values   = 25  and   = .


ANSWER.  The given equation has two solutions  x= 25  and/or  x= .


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

Solved.



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