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16 Apr 2006, 12:03
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Hello,
I'm a bit worried about following
I made first the mistake to simplify as follow : x^4=x^2 by dividing by x^2. Thus, I obtained x^2=1 and solutions=1, -1.
It was false because 0 belongs to the solution.
Since then, I do X^4-X^2=0 => x2(x2-1) sol=-1,0,1
---------------------------------
I've done later the same mistake.
The pb was of that kind : x/y>1.
So I multiplied by y : x*y/y>y => x>y
It was wrong again because there was one solution missing.
The right thing to do is : x/y-1>0 =>(x-y)/y >0 sol= y>0 and x>y or y<0 and x<y.
--------------------------------
So whenever I see such equations, I never divide or multiply to simplify, but put everything on one side.
Today I had an OG11 pb to solve(144)
If (4-x)/(2+x)=x , what is the value of x^2+3x-4?
I did as I learnt and put everything on one side :
(4-x)/(2+x) - x =0 etc... and was right.
As I looked the answer of OG11, I saw that they did as following:
They multiplied both sides by (2+x), yielding 4-x=x(2+x), which is quite faster.
So I'm totally blured, since I thought it was not possible to do that way!
Are there any rule for simplifying such equations?
Thanks for your answers!
I'm a bit worried about following
I made first the mistake to simplify as follow : x^4=x^2 by dividing by x^2. Thus, I obtained x^2=1 and solutions=1, -1.
It was false because 0 belongs to the solution.
Since then, I do X^4-X^2=0 => x2(x2-1) sol=-1,0,1
---------------------------------
I've done later the same mistake.
The pb was of that kind : x/y>1.
So I multiplied by y : x*y/y>y => x>y
It was wrong again because there was one solution missing.
The right thing to do is : x/y-1>0 =>(x-y)/y >0 sol= y>0 and x>y or y<0 and x<y.
--------------------------------
So whenever I see such equations, I never divide or multiply to simplify, but put everything on one side.
Today I had an OG11 pb to solve(144)
If (4-x)/(2+x)=x , what is the value of x^2+3x-4?
I did as I learnt and put everything on one side :
(4-x)/(2+x) - x =0 etc... and was right.
As I looked the answer of OG11, I saw that they did as following:
They multiplied both sides by (2+x), yielding 4-x=x(2+x), which is quite faster.
So I'm totally blured, since I thought it was not possible to do that way!
Are there any rule for simplifying such equations?
Thanks for your answers!
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16 Apr 2006, 12:28
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there is one excerptiong to when you can divide..
if x > 0 then you can divide.. Did the OG say X was greater than 0?
if x > 0 then you can divide.. Did the OG say X was greater than 0?
16 Apr 2006, 12:33
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very good question for an important concept........
here both approaches are correct. if you have inequality, do not cancel or multiply but simply put all variables at one side then solve.....
when you have equation you can canceal/multiply as under:
(4-x)/(2+x)=x
4-x = (2+x) x
2x+x^2 -4+x = 0
x^2 +3x-4 = 0
here both approaches are correct. if you have inequality, do not cancel or multiply but simply put all variables at one side then solve.....
when you have equation you can canceal/multiply as under:
(4-x)/(2+x)=x
4-x = (2+x) x
2x+x^2 -4+x = 0
x^2 +3x-4 = 0
