Question

Solve the following simultaneous equation for x and y
m(x+y) +n(x-y) - (m²+mn+n²) =0
n(x+y) +m(x-y) - (m²-mn+n²) =0

Answer 1

Step-by-step explanation:

Let, (x+y)= T

(x-y)= Z

now, mT+nZ=m²+mn+n²......(1)

nZ+mT=m²-mn+n².......(2)

- - - +. -

2nZ=2mn

Z=2mn/2n

Z=m

put the value of Z in eqñ 1 , we get.

mT+nZ=m²+mn+n²

mT+nm=m²+mn+n²

mT=m²+mn+n²-mn

mT=m²+n²

T=m²+n²/m.

Again,

x+y=m²+n²/m......(3)

x-y=m...................(4)

2x= m²+n²/m-m

2x =n²/m

x=n²/2m answer.

now, put the value of x eqñ 4, we get.

n²/2m-y= m

n²/2m-m=y

y=n²-2m²/2m answer.