Pamela Meyer

2022-01-07

Proof of one inequality

$a+b+c\le \frac{{a}^{3}}{bc}+\frac{{b}^{3}}{ca}+\frac{{c}^{3}}{ab}$

Neil Dismukes

Beginner2022-01-08Added 37 answers

Using Cauchy-Schwarz Inequality twice:

${a}^{4}+{b}^{4}+{c}^{4}\ge {a}^{2}{b}^{2}+{b}^{2}{c}^{2}+{c}^{2}{a}^{2}\ge a{b}^{2}c+b{a}^{2}c+a{c}^{2}b=abc(a+b+c)$

Dawn Neal

Beginner2022-01-09Added 35 answers

I have come up with an answer with myself. Using CS inequality

$({a}^{4}+{b}^{4}+{c}^{4})(1+1+1)\ge {({a}^{2}+{b}^{2}+{c}^{2})}^{2}$

$({a}^{2}+{b}^{2}+{c}^{2})(1+1+1)\ge {(a+b+c)}^{2}$

Hence we have

${a}^{4}+{b}^{4}+{c}^{4}\ge \frac{{(a+b+c)}^{4}}{27}=(a+b+c){\left(\frac{a+b+c}{3}\right)}^{3}\ge abc(a+b+c)$

Hence we have

Vasquez

Expert2022-01-11Added 669 answers

By Holder

Which expression has both 8 and n as factors???

One number is 2 more than 3 times another. Their sum is 22. Find the numbers

8, 14

5, 17

2, 20

4, 18

10, 12Perform the indicated operation and simplify the result. Leave your answer in factored form

$\left[\frac{(4x-8)}{(-3x)}\right].\left[\frac{12}{(12-6x)}\right]$ An ordered pair set is referred to as a ___?

Please, can u convert 3.16 (6 repeating) to fraction.

Write an algebraic expression for the statement '6 less than the quotient of x divided by 3 equals 2'.

A) $6-\frac{x}{3}=2$

B) $\frac{x}{3}-6=2$

C) 3x−6=2

D) $\frac{3}{x}-6=2$Find: $2.48\xf74$.

Multiplication $999\times 999$ equals.

Solve: (128÷32)÷(−4)=

A) -1

B) 2

C) -4

D) -3What is $0.78888.....$ converted into a fraction? $\left(0.7\overline{8}\right)$

The mixed fraction representation of 7/3 is...

How to write the algebraic expression given: the quotient of 5 plus d and 12 minus w?

Express 200+30+5+4100+71000 as a decimal number and find its hundredths digit.

A)235.47,7

B)235.047,4

C)235.47,4

D)234.057,7Find four equivalent fractions of the given fraction:$\frac{6}{12}$

How to find the greatest common factor of $80{x}^{3},30y{x}^{2}$?