AM GM HM inequality

Rarely Tested

Relationship between AM, GM and HM for two numbers a and b,

  • G.M=$$\sqrt{AM \times HM}$$
  • A.M ≥ G.M ≥ H.M
  • The equality holds true if and only if all the terms are equal. (AM = GM = HM)
Question 1

If a,b,c and d are integers such that their sum is 46, then the minimum possible value of $$(a-b)^{2}+(a-c)^{2}+(a-d)^{2}$$ is

Question 2

If X and Y are positive real numbers find the minimum value of $$(X+2Y)*(\frac{1}{X} + \frac{2}{Y}$$)?

Question 3

If X and Y are positive real numbers and 3X+4Y = 14, what is the maximum value of $$X^{3}*Y^4$$ ?

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