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# Inequalities

From the basics to AM-GM and Cauchy-Schwarz.

# A preview of "Inequalities"Join Brilliant Premium

What is the largest real number $$x$$ that satisfies $$2x+3\geq 4x+9$$?

If the product of 5 positive real numbers is 3125, what is the minimum value of their sum?

Let $$a,b,c,d$$ be positive real numbers such that $a+b+c + d = 1.$ What is the minimum value of $\frac{1}{a} + \frac{4}{b} + \frac{9}{c} + \frac{16}{d}?$

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