SOLUTION: Hello,I'm a 9th grade student and I'm stuck at one question.Please help me solve this:- Sqrt(x/1-x)+Sqrt(1-x/x)=13/6 Where (x is not equal to 0,1)

Algebra ->  Radicals -> SOLUTION: Hello,I'm a 9th grade student and I'm stuck at one question.Please help me solve this:- Sqrt(x/1-x)+Sqrt(1-x/x)=13/6 Where (x is not equal to 0,1)      Log On


   

Question 1004483: Hello,I'm a 9th grade student and I'm stuck at one question.Please help me solve this:-
Sqrt(x/1-x)+Sqrt(1-x/x)=13/6
Where (x is not equal to 0,1)
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.
solve
Sqrt(x/1-x)+Sqrt(1-x/x)=13/6
where (x is not equal to 0,1)
--------------------------------

Introduce new variable  y = sqrt%28x%2F%281-x%29%29.
Notice that  1%2Fy = sqrt%28%281-x%29%2Fx%29.

Then your equation takes the form

y + 1%2Fy = 13%2F6.

To solve it,  multiply both sides by 6y.  You will have

6y%5E2 + 6 = 13y.

Simplify:

6y%5E2 - 13y + 6 = 0.

Apply quadratic formula.  You will get the roots  y%5B1%5D = 3%2F2  and  y%5B2%5D = 2%2F3.

Now you need to solve two equations to determine x.

First equation is  sqrt%28x%2F%281-x%29%29 = 3%2F2.
To solve it,  square first both sides.  Then . . .  (. . . as you are 9th grade,  you should know what do next . . . ).

The second equation is  sqrt%28x%2F%281-x%29%29 = 2%2F3.

Please complete the solution yourself.

Good luck!