Inequalties Question (1 Viewer)

[wrxsti]

1/(x-1)(x-3) < -1 any help wud be appreciated :S....

 

[malady]

1/((x-1)(x-3))+1<0
so (x-2)^2/((x-1)(x-3))<0
only soln for this is 1<x<3

 

[malady]

the answer is missing an x between the 1 and 3 .... for some reason its not printing right
<x>
<x></x></x>

 

[Bank$]

Here is my solution, having not done inequalities for sometime i used a purely algebraic approach which can become messy and result in stupid mistakes so if u do find any please post.

EDIT: srry the last part is wrong x cannot be zero so the answer is x greater than 1 and smaller than 2 or x greater than 2 and smaller than 3

Justin

 

[wrxsti]

wow thanx for ur help guys

 

[Yip]

Since no one has pointed it out yet user Bank$, your approach, though mathematically correct, is also inefficient. It is not required to expand the expressions then factorize the cubic. It is much more efficient to go like this:

(x-1)(x-3)+[(x-1)(x-3)]^2<0
(x-1)(x-3)[1+(x-1)(x-3)]<0
(x-1)(x-3)(x^2-4x+4)<0
(x-1)(x-3)(x-2)^2<0
1< x <2, 2< x <3
Note that x cannot equal 2 as the inequality is <, not <=.

 

[kony]

draw the graph of f[x] = 1/(x-1)(x-3)

there's a double root at x=2. and asymptotes at x = 1 and x = 3.

therefore, 1<x<3, excluding 2

 

[~shinigami~]

Since no one has pointed it out yet user Bank$, your approach, though mathematically correct, is also inefficient. Your answer is also partly incorrect. It is not required to expand the expressions then factorize the cubic. It is much more efficient to go like this:

(x-1)(x-3)+[(x-1)(x-3)]^2<0
(x-1)(x-3)[1+(x-1)(x-3)]<0
(x-1)(x-3)(x^2-4x+4)<0
(x-1)(x-3)(x-2)^2<0
1<x<2, 2<x<3
Note that x cannot equal 2 as the inequality is <, not <=.

I need help with a maths question...can you explain your avatar? =p

Love is the primitive of ???

 

[Yip]

Passion, which is a function of time

 

[~shinigami~]

Passion, which is a function of time

Thanks for the help Yip.

 

[Bank$]

Your answer is also partly incorrect.

Where ? If u are talking about x not equal to 2 i added that in right after my post under edit.

(x-1)(x-3)+[(x-1)(x-3)]^2<0
(x-1)(x-3)[1+(x-1)(x-3)]<0
(x-1)(x-3)(x^2-4x+4)<0
(x-1)(x-3)(x-2)^2<0
1< x <2, 2< x <3

I do agree with the inefficientcy of my methord i guess ill have to go back a revise on yr 11 lol.