Question

Answer question number 14 please​

Answer 1

Consider
m = √(x/1-x)
So the equation becomes

m + 1/m = 13/6
So,
6m^2 - 13m + 6 = 0
6m^2 - 9m - 4m + 6 = 0
3m(2m-3)-2(2m-3) = 0
So,
m = 3/2 and m=2/3

So, now,
Take two cases,

m = 3/2. and. m = 2/3
That is,
√x/1-x = 3/2
x/1-x = 9/4
4x = 9 - 9x
x = 9/13

Now, if m= 2/3

√x/1-x = 2/3
x/1-x = 4/9
9x = 4 - 4x
So,
x = 4/13

So, two solution of
x = 4/13 and x = 9/13

Hope this helps you !

Answer 2

Answer:

Consider

m = √(x/1-x)

So the equation becomes

m + 1/m = 13/6

So,

6m^2 - 13m + 6 = 0

6m^2 - 9m - 4m + 6 = 0

3m(2m-3)-2(2m-3) = 0

So,

m = 3/2 and m=2/3

So, now,

Take two cases,

m = 3/2. and. m = 2/3

That is,

√x/1-x = 3/2

x/1-x = 9/4

4x = 9 - 9x

x = 9/13

Now, if m= 2/3

√x/1-x = 2/3

x/1-x = 4/9

9x = 4 - 4x

So,

x = 4/13

So, two solution of

x = 4/13 and x = 9/13

Hope this helps you !