Algebra -1

Hi,

I did this type of question few days ago. If the question mentions greatest possible value, then we can make one of the 2 variables as 0.

eg. x=0;y=3

lets put the values in 2^x + 2^y = x^2 + y^2
2^0+2^3 = 0^2 + 3^2
9=9

So |x-y| = 3.

I would start with some number testing.

if i take 1, its 2 + 2 = 1 + 1 (doesnt work)
if i take 2, its 4 + 4 = 4 + 4 (WORKS) in this case |x-y| = 0

I would also test any combination where x^y = y^x. One I know by solving other similar questions is that 2^4 = 4^2 = 16
so if x = 4 and y = 2, then 2^4 + 2^2 = 4^2 + 2^2 = TRUE

hence |x-y| = 2
hence C

Hi srcc25anu,

your method is rt "I would also test any combination". However in this question it asks greatest possible value. So in my opinion, you answer c)2 is correct in an essence but it not the greatest.
Greatest would be 3.

guerrero wrote:If 2^x + 2^y = x^2 + y^2, where x and y are nonnegative integers, what is the greatest possible value of |x – y|?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

OA3

|x-y| = the DISTANCE between x and y.

To MAXIMIZE this distance, try to MAXIMIZE x and MINIMIZE y.
Note the word in red, which implies that y can be equal to 0.
If y=0, we get:
2^x + 2� = x² - 0²
2^x + 1 = x²
x² - 2^x = 1.

The answer choices imply that the distance between x and y cannot be greater than 4.
If y=0, then x must be equal to one of the following values: 0, 1, 2, 3, 4.
Only x=3 satisfies the equation x² - 2^x = 1:
3² - 2³ = 1.

Thus, x=3 and y=0 satisfy the equation 2^x + 2^y = x^2 + y^2.
In this case, |x-y| = |3-0| = 3.

Given that 2^x + 2^y = x^2 + y^2, if the value of y INCREASES -- if y is equal to an integer GREATER THAN 0 -- then the value of x will have to DECREASE.
The result is that x and y will be brought closer together, DECREASING the distance between them.
Thus, the maximum possible distance between x and y is 3.

The correct answer is D.

rintoo22 wrote:Hi srcc25anu,

your method is rt "I would also test any combination". However in this question it asks greatest possible value. So in my opinion, you answer c)2 is correct in an essence but it not the greatest.
Greatest would be 3.

You are correct. thanks for pointing that out to me.
i missed it.