You can put this solution on YOUR website! x - 3x^1/2 = 4
:
1) x - 3sqrt(x) = 4
Subtract x from both sides
:
-3sqrt(x) = 4 - x
:
square both sides of =
:
9x = (4 - x)^2
:
Expand right hand side of =
:
9x = x^2 - 8x + 16
:
Subtract x^2 - 8x + 16 from both sides
:
-x^2 + 17x - 16 = 0
The left side of = factors
:
-(x - 16) (x - 1) = 0
:
Multiply both sides of = by -1
:
(x - 16) (x - 1) = 0
:
There are two equations
:
x - 16 = 0 or x - 1 = 0
:
x = 16 or x = 1
:
Check x = 1 in equation 1)
:
x - 3 sqrt(x) ⇒ 1 - 3 sqrt(1) = -2
:
x = 1 is incorrect
x - 3 sqrt(x) ⇒ 16 - 3 sqrt(16) = 4
:
x = 16 is correct
:
*******
x = 16
*******
:
----------- Subtracting x from both sides
--- Squaring both sides
------- Subtracting 9x from both sides
0 = (16 - x)(1 - x)
16 - x = 0 OR 1 - x = 0
x = 16 or x = 1
With x = 1 being an EXTRANEOUS solution, we get the only solution as:
