Các câu hỏi tương tự
Gia su a, b, c la cac so duong, chung minh rang: \(\sqrt{\frac{a}{b+c}}+\sqrt{\frac{b}{c+a}}+\sqrt{\frac{c}{a+b}}>2\)
Cho các số thực dương a,b,c,d. Chung minh rang \(\frac{b}{\left(a+\sqrt{b}\right)^2}+\frac{a}{\left(b+\sqrt{a}\right)^2}\ge\frac{\sqrt{bd}}{ac+\sqrt{bd}}\)
Giup mk voi cac ban
cho a,b,c la ba so thuc duong thoa man dieu kien a+b+c=1
chung minh rang P=\(\sqrt{\frac{ab}{c+ab}}+\sqrt{\frac{bc}{a+bc}}+\sqrt{\frac{ca}{b+ca}}\le\frac{3}{2}\)
CHUNG MINH RANG
\(\sqrt[3]{\frac{a}{_b2}}=\frac{\sqrt[3]{ab}}{b}\)
cho \(\hept{\begin{cases}a,b>\frac{\sqrt{5}-1}{2}\\a+b=ab\end{cases}}\)chung minh rang:
\(\frac{1}{a^2+a-1}+\frac{1}{b^2+b-1}\ge\frac{2}{5}\)
\(P=\left(\frac{\sqrt{a}}{\sqrt{ab}-b}+\frac{2\sqrt{a}-\sqrt{b}}{\sqrt{ab}-a}\right):\left(\frac{1}{b\sqrt{a}}-\frac{1}{a\sqrt{b}}\right)\)
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 \(a^2+4b^2=8\)
cho a,b, c > hoac = 0 va a+b+c=1.chung minh
\(\sqrt{a+1}+\sqrt{b+1}+\sqrt{c+1}>3.5\)
2 cho a,b,c >0 . chung minh
\(\frac{a}{b}+\frac{b}{c}+\frac{c}{a}>hoac=3\)
\(B=\frac{1+\sqrt{1-a}}{1-a+\sqrt{1-a}}+\frac{1-\sqrt{1+a}}{1+a-\sqrt{1+a}}+\frac{1}{\sqrt{1+a}}\)
rut gon B
chung minh B luon luon duong vs moi a
chung minh: neu a>0; b>0 thi \(\frac{a+b}{2}\)> hoac= \(\sqrt{ab}\)