Question

Dau coroana , ghidati-va dupa cerinta din imagine si ajutati-ma sa rezolv exercitiul

Answer 1

|x| < 1/a <=> -1/a < x < 1/a si |y| < 1/a <=> -1/a < y < 1/a <=> -2/a < x+y < 2/a si -1/a² < xy < 1/a² => -1 < a²xy < 1 <=> 0 < 1 +a²xy < 2 => | x+y /1+a²xy | <2/a /2=2/a ·1/2 =1/a =1/a .

|z| < 1/a <=> -1/a < z < 1/a <=> -3/a < x+y+z < 3/a si -1/a³ < xyz < 1/a³ => -1/a < a²xyz < 1/a <=> -4/a < x+y+z +a²xyz < 4/a ; -3/a² < xy +xz +yz < 3/a² => -3 < a²·(xy +xz +yz) <3 <=>

-2 < 1+a²·(xy +xz +yz) < 4 => | x +y +z +a²xyz /1 +a²·(xy +yz +yz) | < 4/a /4 =4/a ·1/4 =1/a =1/a .