The second line is a mistake. You can't simplify an equation by squaring each term.
(Original post by lemonpwns1)
x - 3x^(1/2) - 4 = 0
x^2 - 9x - 16 = 0
If you follow the algebra rule "Do the same to the LHS as the RHS" then you can square both sides to get:
But your mistake was in saying that e.g. , which is not true in general.
It's never a good idea to involve a square root in an equation so that's what's lead to your problems. A better method is to rearrange the second equation so that it is in terms of x (or 16x) and substitute that into the first equation.
Try this and then post your working if you're still stuck.
Edit You made a second mistake after your first error. You said that x(x-9)=16 implies that x=16 but this is false. You can only use this method if the right-hand-side is 0 e.g. x(x-9)=0 implies that x=0 or x=9 but e.g. x(x-9)=23 does not imply that x=23 and x=32.
To solve the equation , you would need to use the quadratic formula since it cannot be factorised. But since the equation is false (from the previous error), you don't need to try this.
Last edited by notnek; 23-07-2012 at 05:39.