Trả lời:

5 x 10^25=5x10^25

Học tốt

5*10^25=5*5^25*2^25=5^26*2^25

Christmas is always held (1)_on__ December the twenty fifth every year. Every family is England decorates a Christmas tree and puts (2)_it__ in the middle of the living room. And Santa Claus plays an immportant (3)_role/part__ in this festival. There's a poem to relate him. In 1873, the patron saint of children, Saint Nicholas appeared in a poem (4)_called__ A Visit Saint Nicholas. The character in the poem (5)_was__ a fat jolly man who wore a (6)_red__ suit and gave children (7)_presents/gifts__ on Christmas Eve. The poem, which was (8)_written_ by Clement Clarke Moore, and American professor, became popular (9)_in__ the USA. Santa Claus is based (10)_on__ the description of Saint Nicholas in this poem 

   Christmas is always held (1)__on_ December the twenty fifth every year. Every family is England decorates a Christmas tree and puts (2)_it__ in the middle of the living room. And Santa Claus plays an immportant (3)__role_ in this festival. There's a poem to relate him. In 1873, the patron saint of children, Saint Nicholas appeared in a poem (4)_called__ A Visit Saint Nicholas. The character in the poem (5)_was__ a fat jolly man who wore a (6)_red__ suit and gave children (7)_presents__ on Christmas Eve. The poem, which was (8)_written_ by Clement Clarke Moore, and American professor, became popular (9)_in__ the USA. Santa Claus is based (10)__on_ the description of Saint Nicholas in this poem.

T/ có : B//A , C//A

=> B//C ( tính chất bắc cầu)

*Sao các điểm lại // vs nhau, bn có chắc là đã ghi đúng đề k?*

@33.Nguyễn Minh Ngọc mình cảm ơn bạn, mình ghi đúng đề nha, a,b,c là các đường thẳng chứ ko phải điểm nha

Ta có : \(\frac{x+1}{x-2}=\frac{x+3}{x-4}\)

=> (x + 1)(x - 4) = (x - 2)(x + 3)

=> x² - 4x + x - 4 = x² + 3x - 2x - 6

=> x² - 3x - 4 = x² + x - 6

=> -4x = -2

=> x = 1/2 

Vậy x = 1/2 là giá trị cần tìm

\(\frac{x+1}{x-2}=\frac{x+3}{x-4}\)   

\(\left(đk:\hept{\begin{cases}x-2\ne0\\x-4\ne0\end{cases}}\right)\)   

\(\hept{\begin{cases}x\ne4\\x\ne2\end{cases}}\)   

\(\left(x+1\right)\left(x-4\right)=\left(x-2\right)\left(x+3\right)\)  ( nhân chéo nha )   

\(x^2-4x+x-4=x^2+3x-2x-6\)   

\(x^2-3x-4-x^2+x+6=0\)   

\(-2x+2=0\)   

\(-2x=-2\)   

\(x=1\)

1) are carried out

2) working

3) are 

4) to invent

5) attempts

6) have invented

7) organizing

8) be developed

9) to considered 

10) be wanted

Nowadays, a lot of important inventions are carried out by scientists working for large industrial firms. However, there are still opporunities for other people to invent various things. In Britain, there is a weekly TV program which attemps to show all the devices which people have invented recently. The people organizing the program receive information about 700 inventions per year. New ideas can be developed by private inventors. However, it is important to consider these questions: Will it work? Will it be wanted? Is it new?

Vì x, y > 0

Đặt \(\frac{x}{5}=\frac{y}{4}=k\Rightarrow\hept{\begin{cases}x=5k\\y=4k\end{cases}}\)( k > 0 ) 

x² - y² = 4

<=> ( 5k )² - ( 4k )² = 4

<=> 25k² - 16k² = 4

<=> 9k² = 4

<=> k² = 4/9

<=> k = 2/3 ( vì k > 0 )

=> \(\hept{\begin{cases}x=5\cdot\frac{2}{3}=\frac{10}{3}\\y=4\cdot\frac{2}{3}=\frac{8}{3}\end{cases}}\)

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Nhận thấy x² + 1 \(\ge\)1 > 0 \(\forall\)x

=> \(\left(2x^2-3\right)\left(3x^2-\frac{1}{0,12}\right)\left(x^2+1\right)=0\)

<=> \(\orbr{\begin{cases}2x^2-3=0\\3x^2-\frac{1}{0,12}=0\end{cases}}\Rightarrow\orbr{\begin{cases}2x^2=3\\3x^2=\frac{1}{0,12}\end{cases}}\Rightarrow\orbr{\begin{cases}x^2=\frac{3}{2}\\x^2=\frac{1}{0,36}\end{cases}}\Rightarrow\orbr{\begin{cases}x=\pm\sqrt{\frac{3}{2}}\\x=\pm\frac{1}{0,6}\end{cases}}\)

Vậy \(x\in\left\{\sqrt{\frac{3}{2}};-\sqrt{\frac{3}{2}};-\frac{1}{0,6};\frac{1}{0,6}\right\}\)là giá trị cần tìm

\(\left(2x^2-3\right)\left(3x^2-\frac{1}{0,12}\right)\left(x^2+1\right)=0\)

Nhận thấy rằng x² + 1 ≥ 1 > 0 ∀ x

=> \(\left(2x^2-3\right)\left(3x^2-\frac{1}{0,12}\right)\left(x^2+1\right)=0\)

<=> \(\orbr{\begin{cases}2x^2-3=0\\3x^2-\frac{1}{0,12}=0\end{cases}}\)

+) 2x² - 3 = 0

<=> 2x² = 3

<=> x² = 3/2

<=> x = \(\pm\sqrt{\frac{3}{2}}\)

+) 3x² - 1/0,12 = 0

<=> 3x² - 25/3 = 0

<=> 3x² = 25/3

<=> x² = 25/9

<=> x = \(\pm\frac{5}{3}\)

Vậy S = { \(\pm\frac{5}{3}\); \(\pm\sqrt{\frac{3}{2}}\))