Reference Lê Anh Duy

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

Sherlockkichi will be fined more heavily than the deny error

Otherwise you will get an error

I agree Quoc Tran Anh Le

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

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