If (x^2 - y^2) = 10 and (x + y) = 2, find x and y.

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to solve the equation:

(x^2 - y^2) = 10...(1)

(x + y) = 2...(2)

We know that (x + y)^2 = x^2 + y^2 + 2xy

(2)

=> x + y = 2

=> (x + y)^2 = 4

=> x^2 + y^2 + 2xy = 4

Also from (1)

(x^2 - y^2) = 10

So we have x^2 + y^2 + 2xy - x^2 + y^2 = 4 - 10

=> 2y^2 + 2xy = -6

=> 2y(x+y) = -6

=> 2y(2) = -6

=> y = -3/2

x + y = 2

=> x - 3/2 = 2

=> x = 2 + 3/2

=> x = 7/2

Therefore x = 7/2 and y = -3/2

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Given that:

x^2 - y^2 = 10..............(1)

x+y = 2..............(2)

We need to find the values of x and y.

First , we will rewrite equation (1)

We know that (x^2 - y^2) = (x-y)(x+y)

==> (x-y)(x+y) = 10

But from (2) we know that (x+y) = 2

==> 2 (x-y) = 10

==> x- y = 5................(3)

Now we will solve the system (2) and (3).

We will add (2) and (3).

==> 2x = 7

==> x = 7/2

==> y= 2- x = 2- 7/2 = -3/2

==> y= -3/2

Then the answer is :

x = 7/2 and y = -3/2

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neela | High School Teacher | (Level 3) Valedictorian

Posted on

Q:If (x^2 - y^2) = 10 and (x + y) = 2, find x and y (edited).

A:

x^2-y^2 = 10 given. We know x^2-y^2) = (x+y)(x-y).

=> (x+y)(x-y) = 10.

=> 2(x-y) = 10, as x+y = 2 by data.

=> x-y = 10/2 = 5,

=> x-y = 5.....(2) . And by data  (x+y) = 2....(1)

(2)+(1):  x-y+x+y = 5+2 = y.

=> 2x = 7.

2x/2 = 7/2.

x = 3.5.

(1)-(2) = (x+y-(x-y) = 2- 5 = -3.

=>  2y = -3.

2y/2 = -3/2 = -1.5.

=> y = -1.5.

Therefore x= 3.5 and y = -1.5.

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