$P=1+\frac{1}{x}+\frac{4}{x+1}$

Khi $x$ lớn vô hạn thì $P$ sẽ nhỏ vô hạn nên biểu thức này không có min.

2 + x + 4 + x + ....... + 52 + x = 780

(x + x + .....  x) + (2 + 4 + 6 + ...... + 52) = 780

26 * x + (52 + 2) x 26 : 2 = 780

26 * x + 702 = 780

26 * x = 780 - 720

26 * x = 78

x = 78 : 26

x=  3 

\(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\left(1-\frac{1}{5}\right)\)

\(=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot\frac{4}{5}\)

\(=\frac{1}{5}\)

\(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\left(1-\frac{1}{5}\right)\)

\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.\frac{4}{5}=\frac{1}{5}\)

\(\left(1-\frac{1}{2}\right)\text{ x }\left(1-\frac{1}{3}\right)\text{ x }\left(1-\frac{1}{4}\right)\text{ x }\left(1-\frac{1}{5}\right)\)

\(=\frac{1}{2}\text{ }\text{ x }\frac{2}{3}\text{ x }\frac{3}{4}\text{ x }\frac{4}{5}\)

\(=\frac{1}{5}\)

(x-5)(x²-49)=0

\(\Rightarrow\hept{\begin{cases}x-5=0\\x^2-49=0\end{cases}}\Rightarrow\hept{\begin{cases}x=5\\x=7\end{cases}}\)

Vậy x = 5 hoặc x = 7

x = 5 nha bn 

ủng hộ mik nha  Phạm Hoài An và các bn nữa .

Thank you .............!!

\(\left(x-5\right).\left(x^2-49\right)=0\)

\(\Rightarrow\hept{\begin{cases}x-5=0\\x^2-49=0\end{cases}}\Rightarrow\hept{\begin{cases}x=0+5\\x^2=49\end{cases}\Rightarrow\hept{\begin{cases}x=5\\x^2=7^2=7\end{cases}}}\)

\(\Rightarrow x\in\left\{5;7\right\}\)

5: \(\Leftrightarrow9\left(x^2-5x-4\right)=36\left(x+1\right)+8\left(x^2-10x\right)\)

\(\Leftrightarrow9x^2-45x-36-36x-36-8x^2+80x=0\)

\(\Leftrightarrow x^2-x-72=0\)

=>(x-9)(x+8)=0

=>x=9 hoặc x=-8

6: \(\Leftrightarrow x^2-9=9x-x^2-9+x\)

\(\Leftrightarrow2x^2-10x=0\)

=>2x(x-5)=0

=>x=0 hoặc x=5

5, <=> 9x^2 - 45x - 36 = 36x + 36 + 8x^2 - 80x 

<=> x^2 - x - 72 = 0 <=> x = 9 ; x = -8 

6, <=> x^2 - 9 = 9x - x^2 - 9 + x = 10x - x^2 - 9 

<=> 2x^2 - 10x = 0 <=> x = 0 ; x = 5 

7, <=> (x-1)^2 = (3x+3)^2 

<=> (x-1-3x-3)(x-1+3x+3) = 0

<=> (-2x-4)(4x+2) = 0 <=> x = -2;x=-1/2

8, = (x^2-10x-15)(x^2-10x+25)