Вправа 201 - 300 » 214 (а)

214. Доведи тотожність. а) (x^2- (y-z)^2)/((x+z)^2- y^2 ) + (y^2- (x-z)^2)/((x+y)^2- z^2 ) + (z^2- (x-y)^2)/((y+z)^2- x^2 ) = 1; ((x- y+ z)(x+ y- z))/((x+ z- y)(x+ z+ y)) + ((y- x+ z)(y- x+ z))/((x+ y- z)(x+ y+ z)) + ((z- x+ y)(z+ x- y))/((y+ z- x)(y+ z+ x)) = 1; (x+ y- z)/(x+ y+ z) + (y- x+ z)/(x+ y+ z) + (z+ x- y)/(y+ z+ x) = 1; (x+ y- z+ y- x+ z+ z+ x- y)/(x+ y+ z) = 1; (x+ y+ z)/(x+ y+ z) = 1; 1 = 1. Тотожність доведено.