inequalities with the unknown in the denominator (1 Viewer)

[dlesmond]

Can somebody please help me....I know I probably look like an idiot asking for help but i just can't work through the last step.

I have attatched a .doc file and done most of the working there, I just need help with the last part.

Any help would be greatly appreciated!

 

[Templar]

Draw the parabola out.

In general, x^2+mx+n>0 will have x>a, x<b if a>b are the solutions.

 

[dlesmond]

thankyou for your help....i was so confused over nothing

thats what i love about this site

 

[fishy89sg]

inequalities with the unknown in the denominator

im pretty sure its just called 'further inequalities' lol

 

[dlesmond]

haha is it that's just what it says in my textbook...

 

[fishy89sg]

wow thats lame

what textbook is it

 

[Riviet]

It's probably easier to take out a common factor of 10 from:

50x² -70x + 20 > 0

to get

5x² -7x + 2 > 0

(x-1)(5x-2) > 0, this is easier to graph.

 

[dlesmond]

hey sorry another stupid question going over some last minute things

how can you factorise x^5 - 32

i know you have to reduce it to sum/diff of cubes but how?

ty

 

[airie]

x⁵-32
=(x-2)(x⁴+2x³+4x²+8x+16)

This comes directly from the standard result of xⁿ-yⁿ=(x-y)(x^n-1+x^n-2y+x^n-3y²+...+y^n-1)

 

[muttiah]

these are good questions.. sent u a pm!

 

[muttiah]

i THINK this method might also work.. but i havent expanded it and done it...

and i forgot the formula for that cube thing

x^ 5 - 32

=x^5 - 2^5
=(x+2)(x-2)[x^3 - 2^3]

is this method also correct?

--- nope doesnt work...

 

[airie]

^No, because you're saying that for two numbers a and b, (a^m - b^m)(a^n - b^n)=a^m+n - b^m+n, which is not true. Just expand both sides to verify it.

Btw, for the cubic formula, just sub n=3 into the formula I mentioned above

 

[muttiah]

ah ok.. ur right... but there has to b a simpler way...

 

[airie]

I thought a direct application of a standard result was simple enough

 

[muttiah]

yeah it is... but spose u havent learnt that formula thing... cos i dont remember doing that one... maybe i forgot it..

 

[airie]

Which textbook do you use? I remember seeing it in Cambridge 3u somewhere in Series and Sequences or something...

 

[muttiah]

hmm sequence and series.. yeah i have that book.. but we havent done that section eyt... i think dat we learn that next year.....

any ideas on how to do it without s and s?

 

[airie]

That was chapter 6, I was talking about the prelim book And I don't really think that actually belongs to series and sequences, it's just factorising, they seemed to have just chucked it in randomly Or maybe it was some other chapter? o.0 ... Meh. Somewhere in there. XP

 

[cFsHirLz]

if i didn't know the standard way, i would probably just use the remainder factor theorum and then divide it

 

[SoulSearcher]

That was chapter 6, I was talking about the prelim book And I don't really think that actually belongs to series and sequences, it's just factorising, they seemed to have just chucked it in randomly Or maybe it was some other chapter? o.0 ... Meh. Somewhere in there. XP

6M, for anybody that has the book