This week was full algebra biased!! ðŸ˜„ This is my first time trying inequalities, so this pure beginners level. Do try all the problems first!! And if you guys get any nice solutions , do post in the comments section! These problem uses only Power mean Inequality and Titu's lemma . The First few problems happen to be not problems, but tricks(?) which are extensively used.. Here are the walkthroughs of this week's top 10 Inequality problems! 10th position: Prove that for any real $a>0$ , $a+\frac{1}{a}\ge 2$ Walkthrough: a. only AM-GM 9th position: Prove that for any real $a>0$ , $\frac{a}{1+a^2}\le \frac {a}{2a}$. Walkthrough: a. Only AM-GM b. Use AM-GM to show that $1+a^2\ge 2a $ 8th position: Prove that for any real $x,y>0$ ,$\frac{1}{x+y}\le \frac{1}{4x}+\frac{1}{4y}$ Walkthrough: a. AM-HM inequality (cute ðŸ’–) 7th position : Prove that for any real positive $p,q >0$ and $p+q=1$, then $\left(p+\frac{1}{p} \right)^2+ \left(q+\frac{1}{q} \right)

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