bx+cy=a+b;ax(1/a-b-1/a+b)cy(1/b-a-1/b+a)=2a/a+b

Question

this is a linear equation ques and has to be solved using cross multiplication method

Answer 1

a²-b²=-(b²-a²)=(a-b)(a+b).

ax(2b/(a²-b²)cy(2a/(b²-a²))=-4a²bcxy/(a²-b²)²=2a/(a+b),

-2abcxy/[(a-b)(a²-b²)]=1,

-2abx(a+b-bx)=(a-b)(a²-b²),

2ab²x²-2ab(a+b)x=(a-b)(a²-b²), divide through by 2ab²:

x²-(a+b)x/b=(a-b)(a²-b²)/2ab², complete the square:

x²-(a+b)x/b+¼(a+b)²/b²=(a-b)(a²-b²)/2ab²+¼(a+b)²/b²,

(x-(a+b)/(2b))²=[2(a-b)(a+b)(a-b)+a(a+b)²]/(4ab²),

(x-(a+b)/(2b))²=(a+b)(2(a-b)²+a(a+b))/(4ab²),

(x-(a+b)/(2b))²=(a+b)(3a²-3ab+2b²)/(4ab²),

x=(a+b)/(2b)±√{(a+b)(3a-3b+2b²/a)}/(2b).

bx=(a+b)/2±√{(a+b)(3a-3b+2b²/a)}/2.

bx+cy=a+b, y=(a+b-bx)/c=[(a+b)±√{(a+b)(3a-3b+2b²/a)}]/(2c).