a: Xét ΔABC có 

E là trung điểm của AB

F là trung điểm của AC

Do đó: EF là đường trung bình của ΔABC

Suy ra: EF//BC và \(EF=\dfrac{BC}{2}\)

hay \(EF=\dfrac{7.2}{2}=3.6\left(cm\right)\)

b: Xét tứ giác ADCE có 

F là trung điểm của đường chéo AC

F là trung điểm của đường chéo ED

Do đó: ADCE là hình bình hành 

Suy ra: AE=CD

mà AE=BE

nên CD=BE

giúp mình câu c câu d với

b) Để P nguyên thì \(\sqrt{x}+5⋮3\sqrt{x}-1\)

\(\Leftrightarrow3\sqrt{x}+15⋮3\sqrt{x}-1\)

\(\Leftrightarrow16⋮3\sqrt{x}-1\)

\(\Leftrightarrow3\sqrt{x}-1\in\left\{-1;1;2;4;8;16\right\}\)

\(\Leftrightarrow3\sqrt{x}\in\left\{0;2;3;5;9;17\right\}\)

\(\Leftrightarrow3\sqrt{x}\in\left\{0;3;9\right\}\)

\(\Leftrightarrow\sqrt{x}\in\left\{0;1;3\right\}\)
hay \(x\in\left\{0;1;9\right\}\)

Đề thiếu. Bạn coi lại đề.

Giúp em 2 bài em mới hỏi với ạ. Em cảm ơn ạ

Bạn chụp rõ hơn được không, mờ quá

Ta có \(\widehat{ABC}=\widehat{CAH}\) ( cùng phụ vs \(\widehat{HAB}\) )

Vì tam giác HAC vuông tại H có đường trung tuyến HF

=> HF = 1/2 AC

=> HF = AF

=> tam giác AHF cân tại F

=> góc CAH = góc FHA

Mà góc CAH = góc ABC (cmt)

=> góc ABC = góc FHA

Có OH = OB

=> tam giác OHB cân tại O

=> góc OHB = góc ABC

=> góc FHA = góc OHB

Lại có: góc OHB + góc OHA = 90o

=> góc FHA + góc OHA = 90o

=> góc OHF = 90o

=> OH vuông góc FH

Mà H thuộc (O)

=> FH là tiếp tuyến của (O)

Bài 2: 

Ta có: \(3n^3+10n^2-5⋮3n+1\)

\(\Leftrightarrow3n^3+n^2+9n^2+3n-3n-1-4⋮3n+1\)

\(\Leftrightarrow3n+1\in\left\{1;-1;2;-2;4;-4\right\}\)

\(\Leftrightarrow3n\in\left\{0;-3;3\right\}\)

hay \(n\in\left\{0;-1;1\right\}\)

once upon the time , there was a beautiful princess .she live in a castle on the mountain . one day , a prince passing the castle and he saw that princess.but she guarded by the witch could not get out .the prince withdrew the sword and killed the witch. Finally ,they lived happily togerther forever.

---A golden egg story:

One day a countryman going to the nest of his Goose found there an egg all yellow and glittering.

When he took it up it was as heavy as lead and he was going to throw it away, because he thought a trick had been played upon him.

But he took it home on second thoughts, and soon found to his delight that it was an egg of pure gold.

Every morning the same thing occurred, and he soon becam rich by selling his eggs.

As he grew rich he grew greedy; and thinking to get at once all the gold the Goose could give, he killed it and opened it only to find, nothing.

Greed often overreaches itself: Tham quá thì thâm