Question

solve . x{ a+ b+ab/ a-b } = y{ a+ b -ab/ a+b } , x+y =2a^2 find the value of x and y

Answer 1

-> x{a+ b +ab/(a-b)} =y{a+b-ab/(a+b)}
or, x(a² - b² +ab) /(a-b) =y(a² + 2ab +b² - ab )/(a+b)
or, x(a+b)(a²-b²+ab) =y(a-b)(a²+b²+ab)
or, x(a³ - ab² +a²b +a²b - b³ +ab²) =y(a³ - b³)
or, x(a³ - b³) +2xa²b - y(a³ - b³) = 0
or, (x-y)(a³-b³) +2xa²b =0
or, (x - 2a² +x) (a³-b³) +2xa²b =0 [y = 2a² - x]
or (x - a²) (a³ - b³) + xa²b =0
or, x(a³-b³) +xa²b = a²(a³ - b³)
or, x = a²(a³-b³) /(a³ - b³ +a²b)
So, y = 2a² - x = 2a²- a²(a³ - b³) /(a³ - b³ +a²b)
Hope this is ur required answer.