Would someone please explain the steps for solving this probelm...(x+y)^2 -(x-y)^2=84.?

Question

using foil will be best suited for solving this math problem, I tried to figure out but I ended up getting the wrong answer. So please explain your answer. Thanks

I need to find the value of X+y??

If x and y are positive integers then what is the value of X+y?

Answer 1

(x+y)² - (x-y)² = 84

Multiplying out the squares:

(x² + 2xy + y²) - (x² - 2xy + y²) = 84

Distributing the negative:

x² + 2xy + y² - x² + 2xy - y² = 84

Simplifying:

4xy = 84

Dividing:

xy=21

y=21/x

And that's as simple as it gets

Answer 2

I dojn;t think we have enough here to solve this. However the approach I would take is:

Remember that a^2 - b^2 = (a-b)(a+b)
So

(x+y)^2 - (x-y)^2 = ((x+y)-(x-y))((x+y)+(x-y))
= (x-x + y+y)(x+x+y-y)
= (2y)(2x)
= 4xy

So since

(x+y)^2 -(x-y)^2=84
4xy = 84
xy = 21
x = y / 21

Assuming integral x and y we have
x = 21, y = 1
x = 7, y = 3
x = 3, y = 7
x = 1, y = 21

x = -21, y= -1
x = -7, y = -3
x = -3, y = -7
x = -1, y = -21

Answer 3

Expand the terms

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

Collect like terms together

x^2 - x^2 + 4xy + y^2 - y^2 = 4xy = 84

xy = 21

HTH

Charles

Answer 4

First, expand the terms
(x + y ) ^2 = x^2 + 2xy + y^2
(x - y)^2 = x^2 - 2xy + y^2

Then subtract, to get
2xy + 2xy = 4xy = 84

Divide each side by 4, to get
xy = 21

Divide each side by x, to get
y = 21 / x

Answer 5

Do what everyone else said, but to get a number answer for x or y you have to know the value of one of them first.

Answer 6

(x+y)^2 - (x-y)^2 = 84
(x+y + x-y)(x+y -x+y) = 84
2x.2y = 84
4xy = 84
xy = 21
This is a rectangular hyperbola.

Answer 7

a^2 - b^2 = (a+b)*(a-b)

(x+y)^2 - (x-y)^2 = 84
(x+y+x-y)*(x+y-x+y) = 84
(2x)*(2y) = 84
xy = 21

Without additional info, this is as far as you can get.