Let a, B, C be positive real numbers and prove that: 1 a3+1 b3+1 c3+abc≥2 3．

Let a, B, C be positive real numbers and prove that: 1 a3+1 b3+1 c3+abc≥2 3．

It is proved that because a, B and C are positive real numbers, 1 can be obtained from the mean inequality
a3+1
b3+1
c3≥33 1
a3•1
b3•1
C3
,
1
a3+1
b3+1
c3≥3
abc，
So, 1
a3+1
b3+1
c3+abc≥3
abc+abc，
And 3
abc+abc≥2
Three
abc•abc=2
3，
So, 1
a3+1
b3+1
c3+abc≥2
Three

We know the position of real number ABC on the number axis as shown in the figure - b-a-0-c, which can be simplified as follows: (1) a + C, (2) a ﹣ B ﹣ 2 + a ﹣ b-2bc-2ac; (3) a + C  a  a  a  a  a  a  a  a  a  a  B 

-a-c
c-a-b
a-2c

Simplification of the position of known real number ABC on the number axis As shown in the figure

The original formula = a-2c + b-c-a-b + A-C-B
=a-b-4c

Given that a satisfies the absolute value 2008-A + Radix 2-2009, try to get the square value of a-2088

It should be | 2008-A | + √ (a-2009) = a
Then a-2009 > = 0
So a > = 2009
2008-a<0
So A-2008 + √ (a-2009) = a
√(a-2009)=2008
square
a-2009=2008²
a-2008²=2009

Calculation: (root 6 + 1) 2010 power - 2 (root 6 + 1) 2009 power - 5 (root 6 + 1) 2008 power + 2010

(Gen 6 + 1) ^ 2010-2 (Gen 6 + 1) ^ 2009-5 (Gen 6 + 1) ^ 2008 + 2010 = [(Gen 6 + 1) ^ 2009] (Gen 6 + 1) - 5 (Gen 6 + 1) ^ 2008 + 2010 = [(Gen 6 + 1) ^ 2009] (Gen 6-1) - 5 (Gen 6 + 1) ^ 2008 + 2010 = 5 (Gen 6 + 1) ^ 2008-5 (Gen 6 + 1) ^ 2008 + 2010 = 2010

How much is root 300 equal to

10√3

Why is root number 27 equal to three times root sign 3 Is there a conversion formula?

Geng 27 can be changed into Geng 9 times Geng 3
The number 9 can be changed into 3
So it turns out to be three times the number three
In fact, this is to find whether the divisor of this number can be opened to the full square
It's cooked after doing too much

Root 27 minus one third of root plus root 12 minus four thirds of root

All of them are converted into multiples of root number 3, root number 27 = 3 times root sign 3, root sign 1 / 3 = 3 / 3 root sign 3, root sign 12 = 2 times root sign 3, root sign 4 / 3 = 2 / 3 times root sign 3, so finally equal to (3-1 / 3 + 2-2 / 3) root sign 3 = 4 times root sign 3

2 times root number 5 plus 3 times root number 3 minus root number 5 plus root number 3

2√5+3√3-√5+√3
Original formula = √ 5 + 4 √ 3

How to calculate the third power of (root 3 / 2)

analysis
Count the inside first
（√3/2)
=√6/2
So (√ 6 / 2) 3
=6√6/8
=3√6/4