Question

Answer 1

9,A=\(\dfrac{x}{y}+\dfrac{y}{x}\)+\(\dfrac{xy}{\left(x+y\right)^2}\)=\(\dfrac{x^2+y^2}{xy}\)+\(\dfrac{xy}{\left(x+y\right)^2}\)
=>A≥\(\dfrac{7\left(x+y\right)^2}{16xy}+\left(\right)\dfrac{\left(x+y\right)^2}{16xy}\)+\(\dfrac{xy}{\left(x+y\right)^2}\))
=>A≥\(\dfrac{7}{4}+\dfrac{1}{2}\)=\(\dfrac{9}{4}\)(đpcm)
10,2B=Σ\(\dfrac{2a}{2a+1}\)=>3-2B=Σ\(\left(1-\dfrac{2a}{2a+1}\right)\)=Σ\(\dfrac{1}{2a+1}\)
theo bất đẳng thức C-B-S => 3-2B≥\(\dfrac{9}{2\left(\Sigma a\right)+3}\)=\(\dfrac{9}{6+3}\)=>3-2B≥1
=>-2B≥-2=>2≥2B=>1≥B (đpcm)