Question

Solve for x and y .

( a - b )x + ( a + b )y

= a² - 2ab - b²

( a + b ) ( x + y )

= a² + b² ,

a² is not equal to b².​

Answer 1

Answer

(a−b)x+(a+b ) and=a

2

−2 a b−b

2

----- (i)

(a+b)(x+and )=a

2

+b

2

-------- (ii)

Subtracting eq (i) by eq (ii), we get.

⇒(a−b)x−(a+b)x=a

2

−2 a b−b

2

−a

2

−b

2

⇒−2bx=−2bx(a+b)

⇒x=(a+b)

∴(a+b)(a+b+and )=a

2

+b

2

⇒(a+b)

2

+(a+b ) and=a

2

+b

2

⇒Y=

a+b

- 2 a b

Years.

I hope help u

Answer 2

(a - b)x + (a + b)y = a² - 2ab - b² …(1)

(a + b) (x + y) = a² + b² …(2)

Equation (2) can be written as

(a + b)x+ (a+b) y = a² + b² ….(3)

Now we have to solve equation (1) and (3)

(a - b)x + (a + b)y = a² - 2ab - b² …(1)

(a + b)x+ (a+b)y = a² + b² ...(3)

Subtracting equation (3) from (1) we get

(a - b - a - b) x = a² - 2ab - b²- a² - b²

-2b x = - 2ab -2 b²

-2b x =-2b(a +b)

Dividing both sides by -2b

x = a +b

Now substitude x=a+b in equation (1) we get

(a-b)(a+b) + (a + b) y = a² - 2ab - b²

a² - b² + + (a + b) y = a² - 2ab - b²

Subtracting a² - b² from both the sides

(a + b) y = a² - 2ab - b² - a² + b²

(a + b) y = - 2ab

y = - 2ab /(a+b)

x = a +b , y = - 2ab/(a +b)