Are there any values of X or Y for which (X + Y) squared = Xsquared + Ysquared, Explain Algebraically.?

Question

PLease give me some examples and tell me I need it for math class. Thanks

Answer 1

(x+y)² = x² + y²
x² + 2xy + y² = x² + y²
2xy = 0

If either x or y (or both) is 0, then (x+y)² = x² + y²

Answer 2

Okay this maybe faulty but I’ll give it my best shot.
Given the variables X and Y ranging from 0 to infinity.
And knowing we are substituting in constants.

If might be fair to say that (X +C ) ^2 < X^2.
If so then the same is true for Y. where C>0.
Therefore C has to be equal to zero.
So the answer will would be either X or Y is 0 and X or Y has the range {0,+infinity}.

Answer 3

x=2, y=2

Answer 4

First let's set up an equation, for this that will give all the possibilities of (X+Y)^2=(X^2)+(Y^2).
First let's foil out the left side.
(X+Y)^2=(X+Y)(X+Y)=(X^2)+(2XY)+(Y^2), so, let's set that equal to (X^2)+(Y^2)
(X^2)+(2XY)+(Y^2)=(X^2)+(Y^2), and now moving the right side to the left side(subtracting (X^2)+(Y^2) from both side), you will get:
2XY=0, dividing both sides by 2, you get XY=0
So the only way that can happen is if either X or Y is zero.

So the answer is that X or Y has to be zero in order for:
(X+Y)^2=(X^2)+(Y^2)

Answer 5

x=1 and y=1
so x+y=1+1=2
ans x squared +y squared=1 squared +1 squared =1+1=2
it can also b that x and y are 0.......just plug in 0 in the place of 1 in the above method

Answer 6

one example is x=0 y=1
(0+1)^2 = 0^2+1^2 = 1

actually, if x=0, then any value of y willl work.

Answer 7

(x+y)^2=x^2+2xy+y^2

if (x+y)^2=x^2+y^2

then 2xy=0

x=0 or y=0 or x=y=0

are the solutions

Answer 8

expand (x+y)squared to
x^2 + 2*xy+y^2

setting that equal
x^2+2*xy+y^2=x^2+y^2

and then
2xy=0

so either x or y equals zero