9/18/07 How to pick a method

How to pick a method:
-What characteristics do we use to solve an equation?
-When is it more efficient to us one method over another?


An important side note: For the quiz coming up tomorrow make sure you know how to use each of these methods, and be able to tell why you used the method to solve the problem. Absolute value:
X= 5 for this equation x= 5 or -5
X-3= 5 we are trying to find a way to make this 5, -5
-So what you would need to do is eliminate the absolute value signs, and it will look like this:
X-3= 5 or X-3= -5 so X would be 8 or -2
-You want to get the absolute value alone like you would get a(2) alone
X2+X-6= 4 or X2+X-6= -4 X2+X-10= 0 or X2+X-2= 4
So X=-2,1 or (X+2) (X-1)
If you plugged this into the quadratic it would look like this: -1+/-√1-4(1)(-10)/2

which would equal: -1+/-√41/2 (You could also check your answer graphically.)


Radicals:
(√X-4) 2 =(6) 2 (√X+8) 2 =(X+2) 2
X=40 X-4= 36 X+8= (X+2) 2
X+8= X2 +4x+4
0= X2 +3x+4
(X+4) (X-1)

We have to make sure they both work . 1 would be the actual solution because when you plug -4 back into the original equation it equals 2 and -2
X≠4 X=1

More difficult example:
√X +√2x =4 -make sure you isolate one of the radicals
(√2x) 2 = (4-√x) 2
2x= (4-√x) 2
2x= 16- 8√x +x -divide the whole equation by negative 8
(-1/8 (x-16)) 2 =(√x) 2
1/64 (x2 -32x +256)= X
1/64 x2 -32/64x+ 256/x=X
X2 -32x+256 = 64x
X2 -96x+256= 0 -Use the quadratic formula to finish


Last week we also began talking about inequalities:
Inequalities: divide by (-) or multiply by (-) switch the order
- compound inequality two ways to solve

You can use either method for compound inequalities!
-3<>

x> -7 x≤ 5
-7<>