# A-Level Inequalities HELPP

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#1
I'm completely stuck on how to do this question:
x^2+2y^2<3xy
I started it and i got (x-y)(x-2y)<3xy but I have a feeling I've started in a completely wrong way. I just don't understand where you can go with this question.
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1 month ago
#2
Try bringing everything onto the same side before factorising.
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1 month ago
#3
When you expand the brackets of the expression you've got, you'll see it's different from the question
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1 month ago
#4
(Original post by .Student101.)
I'm completely stuck on how to do this question:
x^2+2y^2<3xy
I started it and i got (x-y)(x-2y)<3xy but I have a feeling I've started in a completely wrong way. I just don't understand where you can go with this question.
This question is a bit different to what you’ve probably done before.After factoring everything to one side you’re left with
(x-y)(x-2y)<0 to give you a better idea of how the graph looks like you would rearrange to get y=x and y= x/2 ,now sketch whilst showing the inequality for each, and then consider the cases of y that’ll lead to the answer.
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#5
(Original post by The A.G)
This question is a bit different to what you’ve probably done before.After factoring everything to one side you’re left with
(x-y)(x-2y)<0 to give you a better idea of how the graph looks like you would rearrange to get y=x and y= x/2 ,now sketch whilst showing the inequality for each, and then consider the cases of y that’ll lead to the answer.
Thank you for your help but as you can see, the question has a <3xy which I'm not sure what to do with.

(Original post by Athy_Obelia)
When you expand the brackets of the expression you've got, you'll see it's different from the question
Oh thank you so much. I didn't realise. But in that case how would I expand it if at all.

(Original post by Pangol)
Try bringing everything onto the same side before factorising.
I tried that and I got x^2+2y^2-3xy<0 but the problem was I just had no idea where to go from there.

I just don't know what to do with question. I'm completely stuck
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1 month ago
#6
What is the actual question and have expanded (and factorized) quadratic expressions like
(x+2y)(2x-3y)
before?

As a route in, you could divide through your inequality by y^2 and substitute z=x/y to get a more usual quadratic in z, which you should be happier with. Then substitute back at the end.
Last edited by mqb2766; 1 month ago
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#7
(Original post by mqb2766)
What is the actual question and have expanded (and factorized) quadratic expressions like
(x+2y)(2x-3y)
before?

As a route in, you could divide through your inequality by y^2 and substitute z=x/y to get a more usual quadratic in z, which you should be happier with. Then substitute back at the end.
The question is just to solve the inequality x^2+2y^2<3xy. I haven't really done much expanding brackets with no numbers so I got a bit confused with that. I don't really understand how you could divide it by y^2 when the equation has 2y^2. And may I ask where the z came from. Sorry if I seem really stupid. I just have no clue with this question.
Last edited by .Student101.; 1 month ago
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1 month ago
#8
(Original post by .Student101.)
The question is just to solve the inequality x^2+2y^2<3xy. I haven't really done much expanding brackets with no numbers so I got a bit confused with that. I don't really understand how you could divide it by y^2 when the equation has 2y^2. And may I ask where the z came from. Sorry if I seem really stupid. I just have no clue with this question.
Can you expand the expression in the previous post? If you can't, there isn't a great deal to be gained from trying the question.

Could you solve
z^2 + 2 < 3z
Can you see the link with the actual question using the previous hints?
Last edited by mqb2766; 1 month ago
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