Tricky problem

[dragonrider]

"If x and y are numbers whose average is 1 and whose difference is 1, what is the product of x and y."
I need help finding the values of x and y. I fairly certain they aren't whole numbers.

 

[pka]

"If x and y are numbers whose average is 1 and whose difference is 1, what is the product of x and y." I need help finding the values of x and y. I fairly certain they aren't whole numbers.

From the given you know: \(\displaystyle |x-y|=1~\&~\dfrac{x+y}{2}=1\) WHY?

Square both sides of each: \(\displaystyle x^2-2xy+y^2=1~\&~x^2+2xy+y^2=4\). HOW?

Now solve those two for \(\displaystyle xy\).

 

[Ishuda]

"If x and y are numbers whose average is 1 and whose difference is 1, what is the product of x and y."
I need help finding the values of x and y. I fairly certain they aren't whole numbers.

Or, without loss of generality, let x be the larger number. Then
x - y = 1
or
x = y + 1

Their average is 1 so
\(\displaystyle \frac{x+y}{2}=\frac{2y+1}{2}=1\)
or
(x, y) = (1.5, .5)
and
xy = 0.75

If y is larger, just swap the values for x and y and the answer for x*y is the same.

 

[dragonrider]

Or, without loss of generality, let x be the larger number. Then
x - y = 1
or
x = y + 1

Their average is 1 so
\(\displaystyle \frac{x+y}{2}=\frac{2y+1}{2}=1\)
or
(x, y) = (1.5, .5)
and
xy = 0.75

If y is larger, just swap the values for x and y and the answer for x*y is the same.

That makes sense. Thanks!

 

[TchrWill]

"If x and y are numbers whose average is 1 and whose difference is 1, what is the product of x and y."
I need help finding the values of x and y. I fairly certain they aren't whole numbers.

Given:

(X + Y)/2 = 1 or X + Y = 2 and

X - Y = 1

Adding X + Y = 2 and X - Y = 1 yields

2X = 3 or X = 1.5 making Y = .5

Therefore, XY = .75