Các câu hỏi tương tự
1. a,b>0, a+b<=1. tìm min P= 1/(a^3+b^3)+1/a^2b+ab^2 ( Dùng BĐT cộng mẫu cho 3 số)
2. a,b,c>0, a^2+b^2+c^2>=1. tìm min P= a+b+c+1/abc
3. x,y,z>0, 1/x+1/y+1/z=4. tìm min P= 1/(2x+y+z)+1/(x+2y+z)+1/(x+y+2z)
a. a,b,c>0, a+b=<1, tìm min P=1/(a^3+b^3)+1/(a^2.b+a.b^2)
b. a,b,c>0,a^2+b^2+c^2=1, tìm minP=a+b+c+1/abc
c. x,y,z>0,1/x+1/y+1/z=4, tìm min P=1/(2x+y+z)+1/(2y+x+z)+1/(2z+x+y)
Cho x>y TM: x+y<=1 CMR: 1/x^2+y^2 = 1/xy>=6
Cho a,b,c >0 TM: a+b+c<=1 CMR: (1/a^2+bc) + (1/b^2+ac)+ 1/c^2+2ab >=9
Cho a,b>0 TM: a+b<=1 ;CMR: (1/a^b^2)+4b+1/ab>=7
Cho a,b>0 TM:a+b<=1. CMR: 1/1+a^2+b^2 +1/2ab >=8/3
Cho a,b,c>0 TM: a+b+c<=3.CMR: 1/a^2+b^2+c^2 +2009/ab+bc+ac >=670
Cho x>y TM: x+y<=1 CMR: 1/x^2+y^2 = 1/xy>=6
Cho a,b,c >0 TM: a+b+c<=1 CMR: (1/a^2+bc) + (1/b^2+ac)+ 1/c^2+2ab >=9
Cho a,b>0 TM: a+b<=1 ;CMR: (1/a^b^2)+4b+1/ab>=7
Cho a,b>0 TM:a+b<=1. CMR: 1/1+a^2+b^2 +1/2ab >=8/3
Cho a,b,c>0 TM: a+b+c<=3.CMR: 1/a^2+b^2+c^2 +2009/ab+bc+ac >=670
Cho x>y TM: x+y<=1 CMR: 1/x^2+y^2 = 1/xy>=6
Cho a,b,c >0 TM: a+b+c<=1 CMR: (1/a^2+bc) + (1/b^2+ac)+ 1/c^2+2ab >=9
Cho a,b>0 TM: a+b<=1 ;CMR: (1/a^b^2)+4b+1/ab>=7
Cho a,b>0 TM:a+b<=1. CMR: 1/1+a^2+b^2 +1/2ab >=8/3
Cho a,b,c>0 TM: a+b+c<=3.CMR: 1/a^2+b^2+c^2 +2009/ab+bc+ac >=670
1 cho 3 số a,b,c tm \(0\le a,b,c\le2\) và\(a+b+c=3\) CM \(a^3+b^3+c^3\le9\)
2 CHO \(x,y,z\in(0,1]\) CM \(\frac{x}{1+y+xz}+\frac{y}{1+z+xy}+\frac{z}{1+x+yz}\le\frac{3}{x+y+z}\)
Cho x>y TM: x+y<=1 CMR: 1/x^2+y^2 + 1/xy>=6
Cho a,b,c >0 TM: a+b+c<=1 CMR: (1/a^2+bc) + (1/b^2+ac)+ 1/c^2+2ab >=9
Cho a,b>0 TM: a+b<=1 ;CMR: (1/a^b^2)+ 4b + 1/ab>=7
Cho a,b>0 TM:a+b<=1. CMR: 1/1+a^2+b^2 + 1/2ab >=8/3
Cho a,b,c>0 TM: a+b+c<=3.CMR: 1/a^2+b^2+c^2 + 2009/ab+bc+ac >=670
tim cac so nguyen a;b;c sao cho: a^2+b^2+c^2+4hoac ab+3b+2c 2. giai phuong trinh: sqrt{2x+3}+sqrt{5-2x}3x^2-12x+14(neu cach giai) 3. tim gia tri nho nhat cua: frac{x+8}{sqrt{x}+1} 4. tim gia tri nho nhat cua: frac{4a}{b+c-a}+frac{9b}{a+c-b}+frac{16c}{a+b-c} 5. cho a;b;c la 3 canh cua tam giac thoa man a+b+c2 ; 0a;b;c1 c/m a^2+b^2+c^2+2abc2 6. giai he phuong trinh 6(x+y)5xy ; 12(y+z)7zy ; 4(...
Đọc tiếp
tim cac so nguyen a;b;c sao cho: a^2+b^2+c^2+4<hoac= ab+3b+2c
2. giai phuong trinh: \(\sqrt{2x+3}+\sqrt{5-2x}=3x^2-12x+14\)(neu cach giai)
3. tim gia tri nho nhat cua: \(\frac{x+8}{\sqrt{x}+1}\)
4. tim gia tri nho nhat cua: \(\frac{4a}{b+c-a}+\frac{9b}{a+c-b}+\frac{16c}{a+b-c}\)
5. cho a;b;c la 3 canh cua tam giac thoa man a+b+c=2 ; 0<a;b;c<1 c/m a^2+b^2+c^2+2abc<2
6. giai he phuong trinh 6(x+y)=5xy ; 12(y+z)=7zy ; 4(z+x)=3xz
7. cho a; b;c la 3 canh cua 1 tam giac c/m voi moi x,y,z \(\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}>\frac{2\left(x^2+y^2+z^2\right)}{a^2+b^2+c^2}\)
8. cho x;y;z>0 thoa man x+y+z=2008 c/m \(\frac{x^4+y^4}{x^3+y^3}+\frac{y^4+z^4}{y^3+z^3}+\frac{z^4+x^4}{z^3+x^3}>hoac=2008\)
1. x, y, z >=0.
Chứng minh rằng: 4(xy+yz+xz)<=Căn((x+y)(y+z)(x+z))(căn(x+y)+căn(y+z)+căn(x+z)).
2. Cho a, b, c>0 thỏa 1/a+1/b+1/c=3.
Tìm GTLN của P=1/căn(a2-ab+b2)+1/căn(b2-bc+c2)+1/căn(c2-ca+a2)