Category Archives: inequality

Curious Inequality: 2^p(|a|^p+|b|^p)>=|a+b|^p

Try out the Personality Quiz! This inequality often appears in Analysis: , for , and . It does seem quite tricky to prove, and using Binomial Theorem leads to a mess and doesn’t work! It turns out that the key … Continue reading

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AM-GM inequality

AM-GM inequality A very useful inequality in Mathematics is the AM-GM Inequality. The arithmetic mean of numbers is . The geometric mean of numbers is . The AM-GM Inequality states that: For any nonnegative numbers , , and equality holds … Continue reading

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