Question

HEY STARS ..!!

★HERE IS YOURS QUESTION★

What is AM - GM inequality in Mathematics ? Explain with reference to an example.

◆ No Spamming

◆ Content Quality

Answer 1

Hey.....!!!!
.
.
☺️☺️☺️
.
.
_Here is Ur Answer_
In mathematics, the inequality of arithmetic and geometric means, or more briefly the AM–GM inequality, states that the arithmetic mean of a list of non-negative real numbers is greater than or equal to the geometric mean of the same list; and further, that the two means are equal if and only if every number in the list is the same.

The simplest non-trivial case — i.e., with more than one variable — for two non-negative numbers x and y, is the statement that

{\displaystyle {\frac {x+y}{2}}\geq {\sqrt {xy}}}

with equality if and only if x = y. This case can be seen from the fact that the square of a real number is always non-negative (greater than or equal to zero) and from the elementary case (a ± b)2 = a2 ± 2ab + b2 of the binomial formula:

{\displaystyle {\begin{aligned}0&\leq (x-y)^{2}\\&=x^{2}-2xy+y^{2}\\&=x^{2}+2xy+y^{2}-4xy\\&=(x+y)^{2}-4xy.\end{aligned}}}

Hence (x + y)2 ≥ 4xy, with equality precisely when (x − y)2 = 0, i.e. x = y. The AM-GM inequality then follows from taking the positive square root of both sides.

.
.
.
Hope it may HELP U
.
.
Plzz Mark it as Brainliest......

Answer 2

Answer:

Step-by-step explanation:

AM≥GM≥HM,where am is arithmetic mean,GM is geometric mean and HM is harmonic mean

Assume two numbers x and y

AM=(x+y)/2

GM=✓(xy)

HM=2xy/(x+y)

Hence, inequality is:

(x+y)/2≥✓xy≥2xy/(x+y)

Hope you understood....