A = m² + n² = (m+n)² - 2mn = 10² - 2 . 5 = 90

B = m³n + m.n³ = mn (m² +n²) = 5 . 90 = 450

C = 1/m + 1/n = \(\dfrac{m+n}{mn}\) = \(\dfrac{10}{5}\) = 2

D = m - n =   \(\sqrt{m^{2^{ }}-2mn+n^2}\) = \(\sqrt{90-5.2}\)= \(\sqrt{80}\) =4\(\sqrt{5}\)

cảm ơn

1. mots dangerous

2. richest

most dangerous

5. Because the weather was cold, we stayed at home

->Because of the cold weather, we stayed at home

6. The teacher is sick, so we have no class tomorrow

->Because the teacher is sick, we have no class tomorrow

->Because of the teacher's sickness, we have no class tomorrow

7. That restaurant is so dirty that nobody wants to eat there.

->Because that restaurant is so dirty, nobody wants to eat there.

->Because of the restaurant's dirt, nobody wants to eat there

8. Because she behaves well, everybody loves her

->Because of her good behaviour, everybody loves her

9. He couldn't come because of his serious illness

->Because he was seriously ill, he couldn't come

5. Because the weather was cold, we stayed at home

->Because of the cold weather, we stayed at home.

6. The teacher is sick, so we have no class tomorrow

->Because the teacher is sick, we have no class tomorrow.

->Because of the sick teacher, we have no class tomorrow.

7. That restaurant is so dirty that nobody wants to eat there.

->Because that restaurant is so dirty, nobody wants to eat there.

->Because of that dirty restaurant, nobody wants to eat there.

8. Because she behaves well, everybody loves her

->Because of her good behavior, everybody loves her.

9. He couldn't come because of his serious illness

->Because he was seriouly ill, he couldn't come.

Bài 1:

\(a-c=m^2+n^2-2mn=\left(m-n\right)^2>0\)

\(\Rightarrow a>c\)

\(a-b=m^2+n^2-m^2+n^2=2n^2>0\)

\(\Rightarrow a>b\)

\(a-\left(b+c\right)=m^2+n^2-\left(m^2-n^2+2mn\right)=2n^2-2mn=2n\left(n-m\right)< 0\)

\(\Rightarrow b+c>a\) mà \(a>b,a>c\)

\(\Rightarrow a,b,c\) là độ dài 3 cạnh của 1 tam giác.

Ta có: \(b^2+c^2=\left(m^2-n^2\right)+4m^2n^2=m^4-2m^2n^2+n^4+4m^2n^2=m^4+2m^2n^2+n^4=\left(m^2+n^2\right)^2\)

\(a^2=\left(m^2+n^2\right)^2\)

\(\Rightarrow a^2=b^2+c^2\)

\(\Rightarrow a,b,c\) là độ dài 3 cạnh của tam giác vuông (định lí Py-ta-go đảo).

Bài 2:

a) \(a^2-b^2-c^2+2bc=a^2-\left(b-c\right)^2=\left(a-b+c\right)\left(a+b-c\right)=\left(2m-2b\right)\left(2m-2c\right)=4\left(m-b\right)\left(m-c\right)\left(đpcm\right)\)

a, Theo định lí Pytago tam giác ABC vuông tại A

\(BC=\sqrt{AB^2+AC^2}=10cm\)

Vì AD là phân giác \(\dfrac{AB}{AC}=\dfrac{BD}{CD}\Rightarrow\dfrac{CD}{AC}=\dfrac{BD}{AB}\)

Theo tc dãy tỉ số bằng nhau 

\(\dfrac{CD}{AC}=\dfrac{BD}{AB}=\dfrac{BC}{AC+AB}=\dfrac{10}{14}=\dfrac{5}{7}\Rightarrow CD=\dfrac{40}{7}cm;BD=\dfrac{30}{7}cm\)

Xét tam giác ABH và tam giác CBA có 

^AHB = ^BAC = 90⁰

^ABH _ chung 

Vậy tam giác ABH ~ tam giác CBA (g.g)

\(\dfrac{AB}{BC}=\dfrac{BH}{AB}\Rightarrow BH=\dfrac{AB^2}{BC}=\dfrac{36}{10}=\dfrac{18}{5}cm\)

-> DH = BD - BH = \(\dfrac{30}{7}-\dfrac{18}{5}=\dfrac{150-136}{35}=\dfrac{14}{35}=\dfrac{2}{5}\)cm 

b, \(\dfrac{AH}{AC}=\dfrac{AB}{BC}\Rightarrow AH=\dfrac{48}{10}=\dfrac{24}{5}cm\)

Vì HM vuông AB; HN vuông AC ; BA vuông AC nên tg AMHN là hcn 

=> AH = MN = 24/5 cm 

c, Xét tam giác AHM và tam giác ABH có 

^HAM _ chung ; ^AMH = ^AHB = 90⁰

Vậy tam giác AHM ~ tam giác ABH (g.g) 

\(\dfrac{AH}{AB}=\dfrac{AM}{AH}\Rightarrow AH^2=AM.AB\)

tương tự tam giác AHN ~ tam giác ACH (g.g)

\(\dfrac{AH}{AC}=\dfrac{AN}{AH}\Rightarrow AH^2=AN.AC\)

=> AM . AB = AN . AC 

Câu c là AM. AB=AN. AC nha mn giúp mik vs 

\(x^3-x^2-x^2+x=0\Leftrightarrow x^3-2x^2+x=0\)

\(\Leftrightarrow x\left(x^2-2x+1\right)=0\Leftrightarrow x\left(x-1\right)^2=0\Leftrightarrow x=0;x=1\)

\(x^2\left(x-1\right)-x^2+x=0\\ \Leftrightarrow x^3-x^2-x^2+x=0\\ \Leftrightarrow x^3-2x^2+x=0\\ \Leftrightarrow x\left(x^2-2x+1\right)=0\\ \Leftrightarrow x\left(x-1\right)^2=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x-1=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)

\(x^2\left(x-1\right)-x\left(x-1\right)=0\)

\(\Leftrightarrow x\left(x-1\right)^2=0\Leftrightarrow x=0;x=1\)

\(A=2\left(x^2-\dfrac{2.1}{4}x+\dfrac{1}{16}-\dfrac{1}{16}\right)+5=2\left(x-\dfrac{1}{4}\right)^2+\dfrac{39}{8}\ge\dfrac{39}{8}\)

Dấu ''='' xảy ra khi x = 1/4 

\(\left(x-3\right)\cdot x+x=2\)

\(x\left(x-3\right)+x=2\)

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

\(x^2-2x=2\)

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

\(x=1+\sqrt{3};1-\sqrt{3}\)

phước Lộc sửa lại đề giúp mik nha=((

Tính chất vật lý : Trạng thái (rắn, lỏng, khí), màu sắc, mùi vị, tính tan, tính dẫn điện, dẫn nhiệt, nhiệt độ sôi (t^o_s), nhiệt độ nóng chảy (t^o_nc), khối lượng riêng (d).

+ Tính chất hoá học: Là khả năng bị biến đổi thành chất khác: Khả năng cháy, nổ, tác dụng với chất khác.