Question

(a-b)x+(a+b)y equal to a square minus 2 a b minus b square
(a+b)(x+y) equal to a square + b square

Answer 1

The value of x = a+b and y = $-(\frac{2\text{a}\tet{b}}{\text{a}+\text{b}})$

Step-by-step explanation:

Given :

(a-b)x+(a+b)y = a²-2ab-b²

(a+b)(x+y) = a²+b²

To find value of x and y

(a-b)x+(a+b)y = a²-2ab-b²

ax-bx+ay+by = a²-2ab-b²

ax+ay-bx+by = a²-2ab-b²

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

(a+b)(x+y) = a²+b² (given)

ax+ay+bx+by = a²+b²

a(x+y)+b(x+y) = a²+b²

a(x+y) = a²+b² - b(x+y) .......................(2)

Substituting value of a(x+y) in equation (1) we get,

a²+b² - b(x+y) + b(y-x) = a²-2ab-b²

b² - bx - by +by - bx = -2ab - b²

b²+ b² - 2bx = - 2ab

2b² + 2ab = 2bx

2b(b+a) = 2bx

x = a+b

Now substituting x = a+b we get

(a+b)(x+y) = a²+b²

(a+b)(a+b+y) = a²+b²

a²+ab+ay+ab+b²+by = a²+b²

2ab+y(a+b) = 0

y(a+b) = - 2ab

$\text{y} = -(\frac{2\text{a}\tet{b}}{\text{a}+\text{b}})$

Hence the value of x = a+b and y = $-(\frac{2\text{a}\tet{b}}{\text{a}+\text{b}})$

To Learn More.....

1. Solve the equation ax^2+ 2abx =0 , a, b is not equal to 0 using factorization ​

https://brainly.in/question/14305925

2. Solve the equation 18x³+81x²+lambda x +60=0,one root being half the sum of the other two. Hence find the value of lambda.

https://brainly.in/question/4790259

Answer 2

ok thanks you so much for give answer