Damon Vazquez

2022-10-09

Proof that $\frac{{a}^{2}}{b}+\frac{{b}^{2}}{c}+\frac{{c}^{2}}{a}\ge a+b+c$

I've tried getting everything on the left side and transforming it into something squared so that I can prove it's bigger or equals to 0 but I've been unsuccessful.

I've tried getting everything on the left side and transforming it into something squared so that I can prove it's bigger or equals to 0 but I've been unsuccessful.

Cullen Kelly

Beginner2022-10-10Added 7 answers

For positives $a$, $b$ and $c$ by C-S we obtain:

$$\sum _{cyc}\frac{{a}^{2}}{b}\ge \frac{{\left(\sum _{cyc}a\right)}^{2}}{\sum _{cyc}b}=\frac{(a+b+c{)}^{2}}{a+b+c}=a+b+c.$$

$$\sum _{cyc}\frac{{a}^{2}}{b}\ge \frac{{\left(\sum _{cyc}a\right)}^{2}}{\sum _{cyc}b}=\frac{(a+b+c{)}^{2}}{a+b+c}=a+b+c.$$

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 $80{x}^{3},30y{x}^{2}$?