Các câu hỏi tương tự
tim gia tri nho nhat cua \(\sqrt{a^2+ab+b^2}+\sqrt{b^2+bc+c^2}+\sqrt{c^2+ac+a^2}\)voi a+b+c=1
Cho a,b,c la cac so thuc t/m (a+2)(b+2)=25/4
Tim gia tri nho nhat cua \(F=\sqrt{1+a^4}+\sqrt{1+b^4}\)
1 cho 3 so thuc duong thoa man x^2010+y^2010+z^20103 tim gia tri lon nhat cua x^2+y^2+z^22 cho a;b;c duong c/m frac{1}{a}+frac{1}{b}+frac{1}{c}hoac3left(frac{1}{a+2b}+frac{1}{b+2c}+frac{1}{c+2a}right)3 tim gia tri nho nhat cua sqrt{a^2+ab+b^2}+sqrt{b^2+bc+c^2}+sqrt{c^2+ac+a^2} voi a+b+c14 cho a;b;c;d va A;B;C;D la cac so duong thoa man frac{a}{A}frac{b}{B}frac{c}{C}frac{d}{D}C/ M sqrt{aA}+sqrt{bB}+sqrt{cC}+sqrt{dD}sqrt{left(a+b+c+dright)left(A+B+C+Dright)}5 tim gia tr...
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1 cho 3 so thuc duong thoa man x^2010+y^2010+z^2010=3 tim gia tri lon nhat cua x^2+y^2+z^2
2 cho a;b;c duong c/m \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}>hoac=3\left(\frac{1}{a+2b}+\frac{1}{b+2c}+\frac{1}{c+2a}\right)\)
3 tim gia tri nho nhat cua \(\sqrt{a^2+ab+b^2}+\sqrt{b^2+bc+c^2}+\sqrt{c^2+ac+a^2}\) voi a+b+c=1
4 cho a;b;c;d va A;B;C;D la cac so duong thoa man \(\frac{a}{A}=\frac{b}{B}=\frac{c}{C}=\frac{d}{D}\)C/ M \(\sqrt{aA}+\sqrt{bB}+\sqrt{cC}+\sqrt{dD}=\sqrt{\left(a+b+c+d\right)\left(A+B+C+D\right)}\)
5 tim gia tri lon nhat cua \(\frac{yz\sqrt{x-1}+xz\sqrt{y-2}+xy\sqrt{z-3}}{xyz}\)
6 phan tich da thuc thanh nhan tu \(y-5x\sqrt{y}+6x^2\)
7 cho x;y;z>0 xy+yz+xz=1 tinh \(x\sqrt{\frac{\left(1+y^2\right)\left(1+z^2\right)}{1+x^2}}+y\sqrt{\frac{\left(1+x^2\right)\left(1+z^2\right)}{1+y^2}}+z\sqrt{\frac{\left(1+x^2\right)\left(1+y^2\right)}{1+z^2}}\)
8 cho a;b;c >0 c/m \(\frac{a}{a+b}+\frac{b}{b+c}+\frac{c}{c+a}
a\Rut gon bieu thuc
b/Tim gia tri nho nhat cua 4A
A=\(\frac{5\sqrt{x}+4}{x+\sqrt{x}-2}+\frac{\sqrt{x}-1}{\sqrt{x}+2}-\)\(\frac{\sqrt{x}+2}{\sqrt{x}-1}\)
1. Cho a,b,c,d la cac so nguyen thoa man \(a^2=b^2+c^2+d^2\)
chung minh rang a.b.c.d + 2015 viet duoc duoi dang hieu cua 2 so chinh phuong.
2. Cho a,b la cac so duong thoa man dieu kien a+b=1. tim gia tri nho nhat cua bieu thuc
\(P=\frac{2+a}{\sqrt{2-a}}+\frac{2+b}{\sqrt{2-b}}\)
Bai 1)Cho bieu thuc Afrac{x+y-2sqrt{xy}}{x-y}a)Tim dieu kien de A co nghiab)Rut gon Ac)Tinh A biet x3+2sqrt{2}va y3-2sqrt{2}Bai 2) Cho bieu thuc Bfrac{x-3}{sqrt{x-1}-sqrt{2}}a)Tim dieu kien de B co nghiab)Rut gon Bc) Tinh B voi x4left(2-sqrt{3}right)d)Tim x de B co gia tri nho nhat
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Bai 1)Cho bieu thuc A=\(\frac{x+y-2\sqrt{xy}}{x-y}\)
a)Tim dieu kien de A co nghia
b)Rut gon A
c)Tinh A biet x=\(3+2\sqrt{2}\)va y=\(3-2\sqrt{2}\)
Bai 2) Cho bieu thuc B=\(\frac{x-3}{\sqrt{x-1}-\sqrt{2}}\)
a)Tim dieu kien de B co nghia
b)Rut gon B
c) Tinh B voi x=\(4\left(2-\sqrt{3}\right)\)
d)Tim x de B co gia tri nho nhat
Cho cac so a, b, c thoa man a2 +b2+c2( <=) 2 .Tim gia tri nho nhat cua bieu thuc S=2015ca-ab-bc
\(P=\left(\frac{\sqrt{a}}{\sqrt{ab}-b}+\frac{2\sqrt{a}-\sqrt{b}}{\sqrt{ab}-a}\right):\left(\frac{1}{b\sqrt{a}}-\frac{1}{a\sqrt{b}}\right)\)
1)chung minh \(P=\sqrt{ab}\)
2) tinh gia tri cua P khi \(a=3-\sqrt{5}\) va b=0,5
3) ting gia tri lon nhat cua P neu \(a^2+4b^2=8\)
P=\(\frac{3\left(x+\sqrt{x}-3\right)}{x+\sqrt{x}-2}+\frac{\sqrt{x}+3}{\sqrt{x}+2}+\frac{\sqrt{x}-2}{1-\sqrt{x}}\\ \)
a, rut gon
b, tim x de P<\(\frac{15}{4}\)
c, tim gia tri lon nhat cua P