Thread: Solve X and Y problem

If x=2 and xy does not =0, what is the value of

x^4*y^4 - (xy)^2 / x^3 * y^2

My answer is 3y^2 / 2y^2...but not sure if that is the answer or should I just say 3/2?

Originally Posted by thecapaccino

If x=2 and xy does not =0, what is the value of

x^4*y^4 - (xy)^2 / x^3 * y^2

My answer is 3y^2 / 2y^2...but not sure if that is the answer or should I just say 3/2?

I assume this problem is
(x^4*y^4 - x^2*y^2)/(x^3*y^2)

I'm not sure where you got 3y^2 / 2y^2, but I don't see that you can get that from this.

If we break up the fraction, we get
(x^4*y^4)/(x^3*y^2) - (x^2*y^2)/(x^3*y^2) = x*y^2 - 1/x

Maybe I'm misunderstanding the problem.

Originally Posted by thecapaccino

If x=2 and xy does not =0, what is the value of

x^4*y^4 - (xy)^2 / x^3 * y^2

My answer is 3y^2 / 2y^2...but not sure if that is the answer or should I just say 3/2?

yes, if that is the answer, you should say 3/2, but how did you get that answer? am i misinterpreting the problem? please type clearly, use brackets to show what is being divided by what.

i think the problem is:

[x^4*y^4 - (xy)^2]/(x^3*y^2)
= [x^4*y^4 - x^2*y^2]/(x^3*y^2)
= [(x^2*y^2)(x^2*y^2 - 1)]/(x^3*y^2)
= (x^2*y^2 - 1)/(x)
= (4y^2 - 1)/2

i plugged in x = 2 in the final step. i didn't split the fraction up as ecMathGeek did

it is a frustrating waste of time when we have to be guessing what the problem is, please, for our sake and yours, state your problems clearly. use parenthesis

Okay...let me try to re-write again. There was a slight typo on the first y^2.


If x=2 and xy does not =0, what is the value of

(x^4)*(y^2) - (xy)^2 / (x^3) * (y^2) =

I plugged in x to get the following

16*(y^2) - 4*(y^2) / 8*(y^2)
then

12*(y^2) / 8*(y^2)
then reduce

3(y^2) / 2(y^2)

Is that still wrong?

Originally Posted by thecapaccino

Okay...let me try to re-write again. There was a slight typo on the first y^2.


If x=2 and xy does not =0, what is the value of

(x^4)*(y^2) - (xy)^2 / (x^3) * (y^2) =

I plugged in x to get the following

16*(y^2) - 4*(y^2) / 8*(y^2)
then

12*(y^2) / 8*(y^2)
then reduce

3(y^2) / 2(y^2)

Is that still wrong?

well, in that case, you are correct. write it as 3/2

Originally Posted by thecapaccino

Okay...let me try to re-write again. There was a slight typo on the first y^2.


If x=2 and xy does not =0, what is the value of

(x^4)*(y^2) - (xy)^2 / (x^3) * (y^2) =

I plugged in x to get the following

16*(y^2) - 4*(y^2) / 8*(y^2)
then

12*(y^2) / 8*(y^2)
then reduce

3(y^2) / 2(y^2)

Is that still wrong?

That is incorrect.
16*(y^2) - 4*(y^2) / 8*(y^2)

= 16y^2 - (4/8)y^2 = 16y^2 - (1/2)y^2 = (31/2)y^2

Unless you meant:

[(x^4)*(y^2) - (xy)^2] / [(x^3) * (y^2)]

in your original problem.

-Dan

[(x^4)*(y^2) - (xy)^2] / [(x^3) * (y^2)] - indeed was what I meant.

I am so sorry for the confusion...I should have put the outside set of parentheses on the numerator problem.

So...bearing that in mind...my answer is correct?

Originally Posted by thecapaccino

[(x^4)*(y^2) - (xy)^2] / [(x^3) * (y^2)] - indeed was what I meant.

I am so sorry for the confusion...I should have put the outside set of parentheses on the numerator problem.

So...bearing that in mind...my answer is correct?

Given that as the form, then I agree with Jhevon, you are correct. (Since xy is not zero then y is not zero so you can legally cancel the y^2.)

-Dan