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Reference Lê Anh Duy

Compact

A = \(\left(a+b+c\right)^2+\left(a+b-c\right)^2-2\left(a-b\right)^2\)

Đk : \(89\le x\le91\)

Applying the Bunhiacopxki inequality

We have : VT \(=1.\sqrt{x-89}+1.\sqrt{91-x}\le\sqrt{\left(1+1\right)\left(x-89+91-x\right)=2}\)

=> VT \(\le2\)

And VP = \(x^2-2.x.90+90^2+2=\left(x-90\right)^2+2\ge2\)

=> VP  \(\ge2\ge\) VT

The sign "=" occurs when and only when: 

\(\left\{{}\begin{matrix}\sqrt{x-89}=\sqrt{91-x}\\x-90=0\end{matrix}\right.\) => \(x=90\)(satisfy)

The answer is 90

El matodora : The Spam question

You should write the real question in English

C1:  We have : 3x + 4x + 5x = x (3 + 4 + 5)

Replace x = 10 <=> 10 ( 3 + 4 + 5) = 10 . 12 = 120

C2 : 3x + 4x + 5x <=> 3 . 10 + 4 . 10 + 5 . 10 = 30 + 40 + 50 = 120

\(P=\left(\dfrac{30}{x}+\dfrac{6x}{5}\right)+\left(\dfrac{y}{5}+\dfrac{5}{y}\right)+\dfrac{4}{5}\left(x+y\right)\ge2.\sqrt{\dfrac{30}{x}+\dfrac{6x}{5}}+2.\sqrt{\dfrac{y}{5}+\dfrac{5}{y}}+\dfrac{4}{5}.10\)

\(P=2.6+2.1+8=22\)

Dấu "=" xảy ra khi \(\left\{{}\begin{matrix}\dfrac{30}{x}=\dfrac{6x}{5}\\\dfrac{y}{5}=\dfrac{5}{y}\\x+y=10\end{matrix}\right.=>\left\{{}\begin{matrix}x^2=25\\y^2=25\\x+y=10\end{matrix}\right.\)

\(=>x=y=5\)

\(Pmin=22< =>x=y=5\)

We have 

\(\dfrac{2}{8}.\dfrac{5}{7}=256.78125=20000000\)

\(=>1000000000:\left(\dfrac{2}{8}.\dfrac{5}{7}\right)=1000000000:20000000=50\)

The answer is 50

We have :  primes from 20 to 30 are 23,29

=> total : 23 + 29 = 52

The answer í 52

\(P=2x+y+\dfrac{30}{x}+\dfrac{5}{y}=\left(x+y\right)\left(\dfrac{5}{x}+\dfrac{5}{y}\right)+\left(\dfrac{25}{x}+x\right)\)

\(\left\{{}\begin{matrix}x>0=>x=\left(\sqrt{x}\right)^2\\y>0=>y=\left(\sqrt{y}\right)^2\end{matrix}\right.\)

\(P1=x+y\ge10\)

\(P2=\dfrac{5}{x}+\dfrac{5}{y}=5.\left(\dfrac{1}{x}+\dfrac{1}{y}\right)\ge5.\dfrac{4}{x+y}=\dfrac{5.4}{10}=2\) khi \(x=y\)

\(P3=\dfrac{25}{x}+x\ge2.\sqrt{\dfrac{25}{x}.x}=2.5=10\) khi \(x=5\)

\(P=\sum P\ge10+2+10=22\) khi \(\left(x;y\right)=\left(5;5\right)\)

Study well

We have:

 1755 . 2 = 3510                                                                                       6019 . 2 = 12038

1755 + 3510 = 4265                                                                                 6019 + 12038 = 18057                                                      

 The answer is :

8426 . 2 = 16852

8426 + 16852 = 25278 

=> ? = 25278

In 6 days, every day do 8h need the number of people is :

6 . 9 : 6 = 9 (people

In 6 days, every day do 9h need the number of people is:

9 . 8 : 9 = 8 (people)

The answer is : 8 people

Let x, y be the length and width of the rectangle:

We have : 

\(\left\{{}\begin{matrix}xy=8\\x=2y\end{matrix}\right.=>\left\{{}\begin{matrix}2y^2=8\\x=2y\end{matrix}\right.< =>\left\{{}\begin{matrix}y=2\left(cm\right)\\x=4\left(cm\right)\end{matrix}\right.\)

So the rectangle width is 2cm

We have a sequence of numbers :

\(12;21;30;39;48;B;66;...\)

The numbers separated by 9 units 

=> B = 48 + 9 = 57

So B = 57

We have :

\(x\left\{{}\begin{matrix}x+x\\x-x\\x.x\end{matrix}\right.< =>0\left\{{}\begin{matrix}0+0\\0-0\\0.0\end{matrix}\right.\)

So x =0

30 machine folding 6 machine is : 

30 : 6 = 5 (machine)

So 30 machines to make 30 wheels need the time :

6 . 5 = 30 (minute)

The answer is : 30 minute

Jane bought a $40 pair of jeans and received a 20% discount, and then bought a $30 shirt and received a 40% discount when she checked out. What is the single percent discount for the total purchase?

Sherlockkichi will be fined more heavily than the deny error

Otherwise you will get an error

I agree Quoc Tran Anh Le

In recent times, Sherlockkichi itself and tick yourself. And I advise you to have the nickname "Cristiano Ronaldo" stop ticking yourself.

Admin punish clearly.

Put : Almors = a

We have:

Brons = a + 20%a = 120%a

Choops = 120%a - 60% = 60%a

<=>\(\dfrac{a}{60\%a}=\dfrac{1}{60\%}=166,\left(6\right)\%\)

The answer is : \(166,\left(6\right)\%\)

We give : Almors is 100

=> Brons  = 100 . (100 . 20%) = 120

=> Choops = 120 . 50% = 60

Percentage of Almors and Choops are:

( 100 . 100 : 60 ) : 100 = 15,(5)%

The answer is : 15,(5)%

We have:

\(\dfrac{10^{11}+10^{10}}{10^{10}}\)

\(< =>\dfrac{10^{10}\left(10+1\right)}{10^{10}}\)

= 11

The answer is : 11

D = (-2x³ - xy²) + (xy² - 1) - (x²y - xy² + 3x²)

Collapse D

Sum of odd-numbered digits ( - ) Sum of even-numbered digits or vice versa is divisible by 11

We have:

(2 + D + D) - (3 + 6 + 9) is divisible by 11

<=> 2 + 2D - 18 is divisible by 11

<=> 2D - 16 is divisible by 11

<=> 2 (D - 8) is divisible by 11

So Greatest common divisor (2 ; 11) = 1

=> D - 8 is divisible by 11

0 \(\le D\le9\)

=> D = 8

So The answer is : 386,892

Find x

\(\left(x-1\right)\left(2x-1\right)=9-x\)

Find x

\(2x^3+6x^2=x^2+3x\)