Cho x,y,z>0, a $\geq \frac{3}{2}$. Chứng minh
$(\frac{x}{y+z})^a +(\frac{y}{x+z})^a + (\frac{z}{x+y})^a \geq \frac{3}{2^a}$
Cho x,y,z>0, a $\geq \frac{3}{2}$. Chứng minh
$(\frac{x}{y+z})^a +(\frac{y}{x+z})^a + (\frac{z}{x+y})^a \geq \frac{3}{2^a}$
Cho x,y,z>0, a $\geq \frac{3}{2}$. Chứng minh
$(\frac{x}{y+z})^a +(\frac{y}{x+z})^a + (\frac{z}{x+y})^a \geq \frac{3}{2^a}$
Áp dụng bất đẳng thức Bernoulli ta có
$$\left(\frac{2x}{y+z} \right )^a\ge \frac{2ax}{y+z}+1-a$$
$$\left(\frac{2y}{x+z} \right )^a\ge \frac{2ya}{x+z}+1-a$$
$$\left(\frac{2z}{x+y} \right )^a\ge \frac{2za}{x+y}+1-a$$
CỘng 3 biểu thức lại ta có rồi ap dụng BĐT Nessbit ta có
$$LHS \ge 3a+3-3a=3$$
Suy ra đpcm.
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Cho x,y,z>0, a $\geq \frac{3}{2}$. Chứng minh
$(\frac{x}{y+z})^a +(\frac{y}{x+z})^a + (\frac{z}{x+y})^a \geq \frac{3}{2^a}$
Áp dụng bdt $\frac{\sum a^{k}}{3}\geq \frac{(\sum a)^{k}}{3^{k}}$
Ta có $VT\geq \frac{(\sum \frac{x}{y+z})^{a}}{3^{a}}\geq \frac{1}{2^{a}}$ ( theo bdt $Neisbit$)
Nên ta có đpcm
$$[\Psi_f(\mathbb{1}_{X_{\eta}}) ] = \sum_{\varnothing \neq J} (-1)^{\left|J \right|-1} [\mathrm{M}_{X_{\sigma},c}^{\vee}(\widetilde{D}_J^{\circ} \times_k \mathbf{G}_{m,k}^{\left|J \right|-1})] \in K_0(\mathbf{SH}_{\mathfrak{M},ct}(X_{\sigma})).$$
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