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inequalities involving cubic equations

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treat it like ordinary equation, make x the subject, then identify the roots.
(careful not to get your inequality sign wrong way around :smile: )
Original post by chatterclaw73
x^2+7x is greater than or equal to 6+2x^3. I can solve this using the factor theorem, but this is a C1 question and the factor theorem isn't supposed to be known at this stage. Is there another way of solving this? Any pointers greatly appreciated.
Reply 21
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Notnek
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Original post by happily
treat it like ordinary equation, make x the subject, then identify the roots.
(careful not to get your inequality sign wrong way around :smile: )

How would you make x the subject?
Original post by Notnek
How would you make x the subject?

for example,
to make x the subject for: x > 5 - x move x to the left-side,
x + x > 5 which becomes 2x > 5 so, x > 5/2 :smile:
Reply 23
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Notnek
21
Original post by happily
for example,
to make x the subject for: x > 5 - x move x to the left-side,
x + x > 5 which becomes 2x > 5 so, x > 5/2 :smile:

It's easy for x > 5-x but not so easy for x^2+7x > 6+2x^3 :smile:
Original post by Notnek
It's easy for x > 5-x but not so easy for x^2+7x > 6+2x^3 :smile:


same principle.
move every x terms to left side:
x^2 +7x -2x^3 >= 6
then maybe you can factorise by x:
x(x+7-2x^2) >=6 and so on
Reply 25
Avatar for Notnek
Notnek
21
Original post by happily
same principle.
move every x terms to left side:
x^2 +7x -2x^3 >= 6
then maybe you can factorise by x:
x(x+7-2x^2) >=6 and so on

What would you do after that? What you're doing is not going to help solve it.

The way to solve this is to move everything to one side and then solve the cubic equation using the factor theorem.
Original post by Notnek
What would you do after that? What you're doing is not going to help solve it.

The way to solve this is to move everything to one side and then solve the cubic equation using the factor theorem.


but the person is not thinking of using factor theorem :smile:
Reply 27
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Notnek
21
Original post by happily
but the person is not thinking of using factor theorem :smile:

I know but what I'm saying is that your method won't work. Please prove me wrong by posting your method in full.
Original post by Notnek
I know but what I'm saying is that your method won't work. Please prove me wrong by posting your method in full.


ooo sorry, move everything across to have zero on the other side then try to factorise the left-hand side if possible.
also you are not wrong :smile:

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