Вправа 301 - 400 » 341

341. Доведи тотожність. б) 1/(x+ y) • (x^2/y + y^2/x) + 1 = (x^2+y^2 )/xy; 1/(x+ y) • (x^3+ y^3)/xy + 1 = (x^2+y^2 )/xy; (x^2+y^2- xy )/xy + 1 = (x^2+y^2 )/xy; (x^2+y^2- xy+ xy )/xy = (x^2+y^2 )/xy; (x^2+y^2 )/xy = (x^2+y^2 )/xy. Тотожність доведено. в) 1/xy + (x2 – xy – (x- y)/〖xy+ y〗^2 ) : (x^2- xy)/(x y) = x + y; 1/xy + ((x^3 y-x^2 y^2+ x^2 y^2- xy^3- + y )/(y(x+ y))) : (x(x-y))/(x+y) = x + y; 1/xy + (〖xy(x〗^2-y^2)-(x- y) )/(y(x+ y)) : (x(x- y))/(x+ y) = x + y; 1/xy + ((x- y)(xy(x+ y)-1))/(y(x+y)) • (x+ y)/(x(x- y)) = x + y; 1/xy + (xy(x+ y)-1)/xy = x + y; (1+ xy(x+y)-1)/xy = x + y; (xy(x+ y))/xy = x + y; x + y = x + y. Тотожність доведено.