doubt

[alltimeacheiver]

ques

what is the value of x^2 + Y^2

1 xy = 16

2 x+y = 10

[Anurag@Gurome]

ques

what is the value of x^2 + Y^2

1 xy = 16

2 x+y = 10

x² + y² = (x + y)² - 2xy. So, to find the value of x² + y², we should know the value of (x + y) and xy.

(1) only gives the value of xy. SO, (1) is NOT SUFFICIENT.

(2) only gives the value of x + y. SO, (2) is NOT SUFFICIENT.

Combining (1) and (2), x² + y² = (10)² - 2(16) = 100 - 32 = 68
So, combining the statements is SUFFICIENT to answer the question.

The correct answer is C.

[alltimeacheiver]

just one doubt here (x-y)^2 can also be equal to x^2 + y^2+2xy. then the value will be differnt. how we can take -2xy standard

[Anurag@Gurome]

just one doubt here (x-y)^2 can also be equal to x^2 + y^2+2xy. then the value will be differnt. how we can take -2xy standard

(x - y)² = x² + y² - 2xy
(x + y)² = x² + y² + 2xy

[alltimeacheiver]

oh great...thanks a lot

[Anurag@Gurome]

oh great...thanks a lot

You are welcome.

[alltimeacheiver]

but still I want to know sir when we are asked about the values of x^2+y^2. in both of the cases as u have also written that (x-y)^2 and (x+y)^2 is equal to x^2 + y^2-2xy and x^2-y^2+2xy respec. then I think the ans should be e. Becoz we canot come to know that when gmat is asking about the the value (x+y)^2 or (x-y)^2. In the both the cases the we have x^2 + y^2. pls clarify liitle bit more.

[Anurag@Gurome]

but still I want to know sir when we are asked about the values of x^2+y^2. in both of the cases as u have also written that (x-y)^2 and (x+y)^2 is equal to x^2 + y^2-2xy and x^2-y^2+2xy respec. then I think the ans should be e. Becoz we canot come to know that when gmat is asking about the the value (x+y)^2 or (x-y)^2. In the both the cases the we have x^2 + y^2. pls clarify liitle bit more.

I think you are a bit confused. We have to find the value of x² + y².
Now, (x - y)² = x² + y² - 2xy
(x + y)² = x² + y² + 2xy
If you look at the statements (1) and (2), we are given the values of xy and x + y. So, here, we use the formula, (x + y)² = x² + y² + 2xy
Note, if we would have the value of x - y then we could have used the formula, (x - y)² = x² + y² - 2xy.

[alltimeacheiver]

so that is what i was expecting sir that the ans should be 100 + 32= 132. not 100-32= 68. I think here I am right.

[Anurag@Gurome]

so that is what i was expecting sir that the ans should be 100 + 32= 132. not 100-32= 68. I think here I am right.

We are using the formula, (x + y)² = x² + y² + 2xy
Now we have to find x² + y²?
We are given xy = 16 and x + y = 10

So, (x + y)² = x² + y² + 2xy implies (10)² = x² + y² + 2 * 16
or 100 = x² + y² + 32
So, x² + y² + 2 = 100 - 32 = 68
I hope this helps?