Generate The Equation of Lines that Through Two Points

Problem
The equation of lines that through (4,1) and (6,-2) is...

Jawaban
from the first point:
x₁=4, y₁=1

from the second point:
x₂=6, y₂=-2

the calculation:

y2-y	=	y2-y1
x2-x		x2-x1
-2-y	=	-2-1
6-x		6-4
-2-y	=	-3
6-x		2
2(-2-y)	=	-3(6-x)
-4-2y	=	-18+3x
-3x-2y+14	=	0
or
3x+2y-14	=	0

The Simplification of The Power Root

Problem

Simplify this equation

( √   ab b4 √   a  ) 1 3

Solution

( √   ab b4 √   a  ) 1 3	=	( a 1 2 b 1 2 ba 1 4  ) 1 3
	=	(a 1 - 1 2 4  b 1 - 1 2  ) 1 3
	=	(a 1 4  b - 1 2  ) 1 3
	=	a 1 12  b - 1 6

The Solution of Two Square plus Two Minus Square

Problem
Jika 2^x+2^-x=5, berapakah nilai 2^2x+2^-2x=...

Solution

2x+2-x	=	5
[2x+2-x]2	=	52	make it square
[2x+2-x].[2x+2-x]	=	52
2x.2x+2x.2-x+2-x.2x+2-x.2-x	=	25
22x+2.2x.2-x+2-2x	=	25
22x+2.2x+(-x)+2-2x	=	25
22x+2.20+2-2x	=	25
22x+2.1+2-2x	=	25
22x+2+2-2x	=	25
22x+2-2x	=	25-2
22x+2-2x	=	23

So the solution is 2^2x+2^-2x=23