This is a blog for my second semester pre-calculus 30s students. Have a blast!

Monday, March 13, 2006

Solving Other Non-linear Equations

let's just have some review!
let's solve for: x2-2x-24 by completing the square, factoring, and using the quadratic formula. Take note...we must get the same answers for all of this.

Completing the square:
x2 -2x-24=0

x2-2x=24
x2 +1=24+1
square root of (x-1)(x-1)=square root of 25
x-1=±square root of 25
x-1=5
x=6,-4

Factoring:
x2-2x-24= 0
(x-6) (x+4)
x= 6,-4

Quadratic formula:


Solve for: y= x4 -2x2 -15

Let p= x2

y= p2 -2p-15

p2-2p-15=0

p2 -2p=15

(p-1)2 =15 +1

square root of (p-1)2 =square root of 16

p-1=± 4

p= -3, 5

substitute p back to x2

x2= square root of -3

x= ± i square root of 3

x= ± square root of 5

Solve for: y= x8-1

Factor x8-1

(x4-1) (x4+1)=0

Factor (x4-1)

(x2-1) (x2+1) (x4+1)=0

(x-1)(x+1)(x2+1)(x4+1)

x-1=0 x+1=0 x2+1=0

x=1 x=-1 x2=-1 x4+1=0

x=± square root of -1 x4=-1

x=± i let p=x2

p2=-1

p=± i

substitute p back to x2

square root of x2=square root of ± i

x=±square root of i

therefore: x= ±1, ± i, ± square root of i

Solve for: y=x3-8

0=x3-8

cube root of x3=cube root of 8

x=2

by: fevie javier


1 Comments:

Blogger John D. - #12 said...

Who's the next scribe then?

9:50 PM

 

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