Question

solve:(a+b)x+(a-b)y=a^2+b^2 and (a-b)x+(a+b)y=a^2+b^2 
the person who answer first to this question will be rewarded brainly answer

Answer 1

Given equations,
(a+b)x+(a-b)y=a²+b²...........................1

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

Multiplying eq1 by (a-b) we get,
(a²-b²)x+(a-b)²y=(a²+b²)(a-b)............3

Multiplying eq2 by (a+b) we get,
(a²-b²)x+(a+b)²y=(a²+b²)(a+b)..........4

By eq3-eq4 we get ,
(a²-b²)x+(a-b)²y-(a²-b²)x-(a+b)²y=
(a²+b²)(a-b) -(a²+b²)(a+b)

a²y+b²y-2aby-a²y-b²y-2aby=
(a²+b²){a-b-a-b}

-4aby=(a²+b²)(-2b)

y=(a²+b²)(-2b)/-4ab

y=(a²+b²)/2a......................................5
Putting eq5 in eq1 we get,
(a+b)x+(a-b){(a²+b²)/2a}=a²+b²

(a+b)x=(a²+b²)-(a-b)(a²+b²)/2a

(a+b)x=(a²+b²){1-(a-b)/2a}

(a+b)x=(a²+b²){2a-a+b)/2a

(a+b)x=(a²+b²)(a+b)/2a

x=(a²+b²)/2a

Hence, x=y=(a²+b²)/2a.

Answer 2

Answer:

x=a^2+b^2/2a

y=a^2+b^2/2a

So x ans y are equal