SOLUTION: 4x − 11x^1/2 + 6 = 0 Showing all necessary working, solve the equation

Question 1152545: 4x − 11x^1/2 + 6 = 0
Showing all necessary working, solve the equation
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.


Introduce new variable  y = .


Then your equation takes the form


    4y^2 - 11y + 6 = 0.


Solve this quadratic equation using the quadrtic formula


     =  =  = .



Case 1.   =  =  = 2.


         Then   = 2;  hence,  x = 4.



Case 2.   =  =  = .


         Then   = ;  hence,  x = .


ANSWER.  The given equation has two and only two solutions:  x= 4  and  x= .

Solved, answered and explained in most detailed way, as requested. And completed.

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Introducing new variable is a standard way of solving such equations.

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