Вправи: 341

341. Доведи тотожність.

б) 1x+ y • (x2y + y2x) + 1 = x2+y2 xy; 1x+ y • x3+ y3xy + 1 = x2+y2 xy;

x2+y2- xy xy + 1 = x2+y2 xy; x2+y2- xy+ xy xy = x2+y2 xy; x2+y2 xy = x2+y2 xy.

Тотожність доведено.

в) 1xy + (x² – xy – x- yxy+ y2) : x2- xyx y = x + y;

1xy + (x3y-x2y2+ x2y2- xy3- + y y(x+ y)) : x(x-y)x+y = x + y;

1xy + xy(x2-y2)-(x- y) y(x+ y) : x(x- y)x+ y = x + y;

1xy + (x- y)(xyx+ y-1)y(x+y) • x+ yx(x- y) = x + y; 1xy + xyx+ y-1xy = x + y;

1+ xyx+y-1xy = x + y; xy(x+ y)xy = x + y; x + y = x + y.

Тотожність доведено.