Các câu hỏi tương tự
\(\left(\frac{\sqrt{14}-\sqrt{7}}{1-\sqrt{2}}+\frac{5-\sqrt{5}}{1-\sqrt{5}}\right):\frac{1}{\sqrt{7}-\sqrt{5}}\)
Tinh gia tri bieu thuc
cho bieu thuc \(P=\left(\frac{\sqrt{x}-2}{x-1}-\frac{\sqrt{x+2}}{x-2\sqrt{x}+1}\right)\cdot\frac{\left(1-x\right)^2}{2}\)
a) rut gon P
b) tim gia tri lon nhat cua P
Cho bieu thuc: \(p=\left(\frac{1}{\sqrt{x}-\sqrt{x-1}}-\frac{x-3}{\sqrt{x-1}-\sqrt{2}}\right)\left(\frac{2}{\sqrt{2}-\sqrt{x}}-\frac{\sqrt{x}+\sqrt{2}}{\sqrt{2x}-x}\right)\)
a) Tim DKXD cua bieu thuc p
b) Rut gon bieu thuc p
Cho x,y la cac so thuc duong. Tim gia tri nho nhat cua bieu thuc:
\(P=\frac{xy}{x^2+y^2}+\left(\frac{1}{x}+\frac{1}{y}\right)\sqrt{2\left(x^2+y^2\right)}\)
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 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...
Đọc tiếp
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}
\(M=\left(\frac{\sqrt{x}+2}{x+2\sqrt{x}+1}-\frac{\sqrt{x}-2}{x-1}\right)N=\frac{\sqrt{x}+1}{\sqrt{x}}\) voi x>0 va x khac 1
a) tim gia tri bieu thuc cua N khi x = 25
b) rut gon S = M.N
c) tim m de S<-1
tim gia tri lon nhat cua bieu thuc\(\frac{1}{3x-2\sqrt{6x}+5}\)
Tinh gia tri cua bieu thuc : a) A = \(\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+\frac{1}{\sqrt{4}+\sqrt{5}}+...+\frac{1}{\sqrt{24}+\sqrt{25}}\)
b) B = \(\frac{1}{\sqrt{3}+\sqrt{5}}+\frac{1}{\sqrt{5}+\sqrt{7}}+\frac{1}{\sqrt{7}+\sqrt{9}}+...+\frac{1}{\sqrt{97}+\sqrt{99}}\)