Giúp em với

Do AM là đường cao \(\Rightarrow AM\perp BC\Rightarrow\widehat{BMH}=90^0\)

Tương tự BN là đường cao nên \(\widehat{BNC}=90^0\)

Xét hai tam giác BMH và BNC có:

\(\left\{{}\begin{matrix}\widehat{MBH}-chung\\\widehat{BMH}=\widehat{BNC}=90^0\end{matrix}\right.\)

\(\Rightarrow\Delta BMH\sim\Delta BNC\left(g.g\right)\)

\(\Rightarrow\dfrac{BH}{BC}=\dfrac{BM}{BN}\Rightarrow BH.BN=BM.BC\)

Vận tốc dòng nước là:

\(30-27=3\) (km/h)

Vận tốc con thuyền khi con thuyền ngược dòng từ B về A là:

\(27-3=24\) (km/h)

Thời gian con thuyền ngược dòng từ B về  A là:

\(120:24=5\) (giờ)

Here's an introduction to the Battle of Dien Bien Phu in English:

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The Battle of Dien Bien Phu was a pivotal conflict in the First Indochina War, marking the climax of a struggle between French colonial forces and the Viet Minh, led by Uncle Ho Chi Minh. This battle took place between March and May 1954 in the Dien Bien Phu valley in northwestern Vietnam.

The French, under the command of General Christian de Castries, fortified the Dien Bien Phu valley, creating a complex series of strongpoints to defend against the expected Viet Minh assault. 

However, the Viet Minh, commanded by General Vo Nguyen Giap, executed an impressive logistical feat. They transported heavy artillery and supplies over mountainous terrain, manually hauling pieces through rugged paths. Once in position, they launched a massive and well-coordinated attack on the French positions, encircling and bombarding them with artillery, which the French had believed impossible.

The siege lasted for fifty-five days, with intense fighting characterized by trench warfare and direct assaults reminiscent of World War I battles. The Viet Minh's tactics and endurance in the face of French firepower eventually led to the fall of the French garrison.

The capture of Dien Bien Phu was a significant victory for the Viet Minh and a symbol of the rise of nationalist movements in colonial territories. It precipitated the Geneva Conference, which negotiated the ceasefire and eventually led to the withdrawal of French forces from Indochina. This battle not only marked the end of French colonial rule in Vietnam but also reshaped the geopolitical landscape of Southeast Asia.

Dien Bien Phu remains a testament to the strategic brilliance of General Giap and the resilience of the Vietnamese people. It stands as a historic reminder of the challenges of colonial warfare and the potent force of nationalist fervor.

Các số lẻ ko chia hết cho 3 có dạng \(6k+1\) hoặc \(6k+5\)

TH1: m, n cùng có dạng \(6k+1\Rightarrow\left\{{}\begin{matrix}m=6a+1\\n=6b+1\end{matrix}\right.\) với a;b nguyên

\(\Rightarrow n^2-m^2=\left(6a+1\right)^2-\left(6b+1\right)^2=12\left(a-b\right)\left(3\left(a+b\right)+1\right)\)

- Với a;b cùng tính chẵn lẻ \(\Rightarrow a-b\) chẵn \(\Rightarrow a-b\) chia hết cho 2 \(\Rightarrow12\left(a-b\right)⋮24\)

\(\Rightarrow n^2-m^2⋮24\)

- Với a;b khác tính chẵn lẻ \(\Rightarrow3\left(a+b\right)\) lẻ \(\Rightarrow3\left(a+b\right)+1\) chẵn \(\Rightarrow12\left(3\left(a+b\right)+1\right)⋮24\)

\(\Rightarrow n^2-m^2⋮24\)

TH2: n;m cùng dạng \(6k+5\) hay \(\left\{{}\begin{matrix}n=6a+5\\m=6b+5\end{matrix}\right.\)

\(n^2-m^2=12\left(a-b\right)\left[3\left(a+b\right)+5\right]\)

Tương tự như trên:

a, b cùng chẵn lẻ thì \(a-b\) chẵn; a, b khác tính chẵn lẻ thì \(3\left(a+b\right)+5\) chẵn

TH3: 1 số có dạng \(6k+1\), 1 số có dạng \(6k+5\)

\(\Rightarrow\left|n^2-m^2\right|=\left|\left(6a+1\right)^2-\left(6b+5\right)^2\right|=12\left|\left(a-b\right)\left[3\left(a+b\right)+1\right]-2\left(2b+1\right)\right|\)

a,b cùng chẵn lẻ thì \(a-b\) chẵn; a,b khác tính chẵn lẻ thì \(3\left(a+b\right)+1\) chẵn nên \(\left(a-b\right)\left[3\left(a+b\right)+1\right]-2\left(2b+1\right)\) luôn chẵn

a: Đề sai rồi bạn

b: \(n^5-n=n\left(n^4-1\right)\)

\(=n\left(n^2-1\right)\left(n^2+1\right)\)

\(=n\left(n-1\right)\left(n+1\right)\left(n^2+1\right)\)

Vì n;n-1;n+1 là ba số nguyên liên tiếp

nên \(n\left(n-1\right)\left(n+1\right)⋮6\)

=>\(n\cdot\left(n-1\right)\left(n+1\right)\left(n^2+1\right)⋮6\)

=>\(n^5-n⋮6\)

Vì 5 là số nguyên tố

nên \(n^5-n⋮5\)

Ta có: \(n^5-n⋮5;n^5-n⋮6\)

mà ƯCLN(5;6)=1

nên \(n^5-n⋮5\cdot6\)

=>\(n^5-n⋮30\)