Bai 09 BTTL BDT cosi p9

Khoá h c BDHSG Chuyên đ B t đ ng th c – Th y Tr n Ph B T ng B t đ ng th c Cô - si NG TH C CÔ-SI (PH N 07) BÀI T P T LUY N Giáo viên: TR N PH NG Các t p tài li u đ c biên so n kèm theo gi ng B t đ ng th c Cô - si (Ph n 09) thu c khóa h c B i d ng h c sinh gi i Chuyên đ B t đ ng th c – Th y Tr n Ph ng t i website Hocmai.vn c n h c tr c gi ng sau làm đ y đ t p tài li u s d ng hi u qu , b n BÀI T P ÁNH GIÁ M U S Let be given a, b > Prove that a b   2 ab a b b a Let be given a, b, c > Prove that 2a 2b 2c 1      4 4 a b b c c a a b c Let be given a, b, c > satisfying abc = Prove that ab bc ca   1 5 a  b  ab b  c  bc c  a  ca Let be given a, b, c > satisfying abc = Prove that a  b9 b9  c c9  a   2 a  a b3  b b  b3 c  c c  c a  a Let be given a, b, c > satisfying abc = Prove that a b2 b2 c c2 a   1 a b  a  b7 b c  b7  c c a  c  a Let be given a, b, c > satisfying a + b + c = Prove that 2a 2b2 2c    2 (1  a )(1  a ) (1  b)(1  b ) (1  c)(1  c ) a , b, c  Given  abc  Prove that a2 b2 c2   1 a  b  b3c b  c  c3a c  a  a 3b 2 Let be given a, b, c satisfying a + b + c  Prove that a  bc  b  ca  c  ab  b  ca Let be given a , b, c > Prove that c  ab a  bc a  bc  b2  ca  c  ab  (1) 2 2 2  a  b  c abcb  c  abcc  a  abca  b  10 Let be given a, b, c satisfying a > b > c Prove that 1 17408    7 7 ( a  b) ( a  c ) (b  c) (b  a ) (c  a ) (c  b) (a  c)14 Giáo viên : Tr n Ph Ngu n Hocmai.vn – Ngơi tr ng chung c a h c trò Vi t T ng đài t v n: 1900 58-58-12 : ng Hocmai.vn - Trang | -