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x>y x^2 - 1> y^2 -4y +x - 1 Which of the following [#permalink]
27 Jan 2008, 10:30

x>y

x^2 - 1> y^2 -4y +x - 1

Which of the following represents all the possible values of y?

y>=0 y>0 y>1 y>7 y>8

Let us first simplify the inequality. Cancel out the (-1) from both sides and move the x over to the left hand side:

x^2- x>y^2 - 4y

from then I can't catch any passage of the explaantion:

x(x-1)>y(y-4) (y+1)(y+1-1)>y(y-4) 1>4

then it is said that Then it is said in the explanation that when we divided both parts of the equation by , we assumed that it is greater than 0. Since at the end we are left without a variable, this means that the equation works for any value where y>0

what's the meaning of this? explanations appreciated.

The fact that the equation can be broken down to x^2 - x > y^2 - 4y means that any positive number (any y>0) makes the equation on the right negative so the answer must be B

Very good! Thanks

yes, I didn't consider that x and y were consecutive positive integers

Which of the following represents all the possible values of y?

y>=0 y>0 y>1 y>7 y>8

Let us first simplify the inequality. Cancel out the (-1) from both sides and move the x over to the left hand side:

x^2- x>y^2 - 4y

from then I can't catch any passage of the explaantion:

x(x-1)>y(y-4) (y+1)(y+1-1)>y(y-4) 1>4

then it is said that Then it is said in the explanation that when we divided both parts of the equation by , we assumed that it is greater than 0. Since at the end we are left without a variable, this means that the equation works for any value where y>0

what's the meaning of this? explanations appreciated.

You can try values.

x>y. Thus lets say that x=.1 and y=0. This cannot work b/c the left side would be negative.

Assume we have: x(x-1)>y(y-4)

We need to make it so the left side has a the minimum value, while keeping it bigger than the right side.

Make x=1. Thus the left side is 0. This is the min value we can create here for the left side. Since y cannot equal 0, the next best thing is y>0.

Which of the following represents all the possible values of y?

y>=0 y>0 y>1 y>7 y>8

Let us first simplify the inequality. Cancel out the (-1) from both sides and move the x over to the left hand side:

x^2- x>y^2 - 4y

from then I can't catch any passage of the explaantion:

x(x-1)>y(y-4) (y+1)(y+1-1)>y(y-4) 1>4

then it is said that Then it is said in the explanation that when we divided both parts of the equation by , we assumed that it is greater than 0. Since at the end we are left without a variable, this means that the equation works for any value where y>3/2

what's the meaning of this? explanations appreciated.

In m02 the explanation reads y>3/2 instead of y>0. I think its only a typo. Can someone pls confirm.