Chuyªn ®Ò: BÊt ®¼ng thøc ************* Bµi to¸n 1: Cho a>b vµ ab=1. Chøng minh r»ng: 2 2 2 2 a b a b + ≥ − Bµi to¸n 2: Cho 1 ; ; 0;0 , , 2 x y z p q r> < ≤ ; x+y+z=p+q+r=1. a) CMR: nÕu x y z≤ ≤ th× 2 x y px qy rz + + + ≥ b) CMR: 8px qy rz xyz+ + ≥ Bµi to¸n 3: Cho 0; 0a c b c≥ ≥ ≥ ≥ . CMR: ( ) ( )c a c c b c ab− + − ≤ Bµi to¸n 4: a) Cho ; 1.a b ≥ CMR: 1 1a b b a ab− + − ≤ b) Cho , , 0a b c ≥ vµ a+b+c=1. CMR: 8 ( )( )( ) 729 P bc a b b c c a= + + + ≤ Bµi to¸n 5: Cho , , 0a b c > vµ a+b+c=1. CMR: 2 2 2 1 1 1 9 2 2 2a bc b ac c ab + + ≥ + + + Bµi to¸n 6: Cho , , 0a b c > . CMR: 2 2 2 1 1 1 a b c a bc b ac c ab abc + + + + ≤ + + + Bµi to¸n 7: Cho , , 0a b c > vµ a+b+c=1. CMR: 2 2 2 1 1 1 1 30 a b c ab bc ca + + + ≥ + + Bµi to¸n 8: Cho a, b, c >0. CMR: 3 3 3 2 2 2 2 2 2 3( )a b c ab bc ca b bc c c ca a a ab b a b c + + + + ≥ − + − + − + + + Bµi to¸n 9: Cho a, b, c>0. CMR: 2 2 2 2 a b c a b c b c c a a b + + + + ≥ + + + Bµi to¸n 10: Cho a, b, c >0. CMR: 3 3 3 2 2 2 a b c a bc b ac c ab+ + ≥ + + Bµi to¸n 11: Cho a, b, c >0. CMR: 3 3 3 3 3 3 2( ) b c c a a b ab bc ca a b c + + + + + ≥ + + Bµi to¸n 12: Cho a, b, c >0. CMR: 2 2 2 a b c a b c b c a + + ≥ + + Bµi to¸n 13: Cho a,b,c >0 vµ abc=1. CMR: 1 1 1 1 1 1 1a b b c c a + + ≤ + + + + + + Bµi to¸n 14: Víi a,b,c>0. CMR: 1 1 1 3 3 3 2 2 2a b c a b b c c a + + ≥ + + + + + Bµi to¸n 15: Cho a, b, c >0. CMR: 2 2 a b a b b a + ≥ + Bµi to¸n 16: Cho a, b, c >0 vµ abc=1. CMR: 3 3 3 1 1 1 ( ) ( ) ( ) 2 ab bc ca a b c b c a c a b + + + + ≥ + + + Bµi to¸n 17: Cho a, b, c >0. CMR: 2 3 2 2 2 1 c b a b c ac ab b ac + + ≥ + + http://violet.vn/tranthuquynh81