ta có (a+b+c)(1/a+1/b+1/c)=1+b/a+c/a+a/b+1+c/b+a/c+b/c+1=3+(a/b+b/a)+(a/c+c/a)+(b/c+c/b)
ta có (a-b)2>0suy ra a/b+b/a> hoặc =2
suy ra (a+b+c)(1/a+1/b+1/c)>hoặc=9
suy ra 1/a+1/b+1/c>hoặc=9/a+b+c
cao nhan naoo giup em voi
1.cmr voi a,b,c la cac so duong ta co: (a+b+c)(1/a+1/b+1/c)>hoac =9
2.giai bat phuong trinh (x+3)(x-3),(x-2)^2+3
EM XIN CHAN THANH CAM ON CAC VI CAO NHAN >_<
c/m voi 3 so thuc tuy y ta co
a2 cong b2 cong 1 lon hon hoac bang ab cong a cong b
CMR voi a,b,c la cac so duong, ta co (a+b+c)(1/a+1/b+1/c)>=9
chung minh rang voi a,b,c la cac so duong ,ta co (a+b+c)(1/a+1/b+1/c)>=9
voi moi so a b c tuy y. CMR: a^2 + b^2 + c^2 > hoac = 2ab - 2ac + 2bc
c/m
x+1/x> hoac=2 voi moi x>0
c/m voi moi x,y>0 ta co
x5+y5>hoac= x4y+xy4
a) a/b + b/a >_ 2
b) (a+b)(1/a +1/b)>_ 4
c) (a+b+c) (1/a +1/b +1/c)>_9
2. chung minh rang moi a, b la cac so tuy y, ta co :
a) (a-1)(a-3)(a-4)(a-6) +9 >_ 0
b) 4a(a-b)(a+1)(a+b+1) + b2 >_ 0
3. giai phuong trinh | x2 - x + 2| - 3x + 7 = 0
cmr : a^2/b^2 +b^2/c^2+c^2/a^2 luon luon lon hon hoac bang c/b+ b/a+ a/c voi a,b,c lon hon 0
