Ta có: \(4 H \left(\right. x \left.\right) = \left(\right. 2 x \left.\right)^{2} - 2.2 x . y + y^{2} + 3 y^{2} - 4 x + 4 y + 4\)

\(= \left(\right. 2 x - y \left.\right)^{2} - 2 \left(\right. 2 x - y \left.\right) + 3 y^{2} + 2 y + 3 + 1\)

\(= \left(\right. 2 x - y - 1 \left.\right) + 3 \left(\right. y^{2} + \frac{2}{3} y + 1 \left.\right)\)

\(= \left(\right. 2 x - y - 1 \left.\right) + 3 \left(\left(\right. y + \frac{1}{2} \left.\right)\right)^{2} + \frac{8}{3} \geq \frac{8}{3}\).

Vậy giá trị nhỏ nhất của \(E\) là: \(\frac{8}{3} : \&\text{nbsp}; 4 = \frac{2}{3}\) tại \(x = \frac{2}{3} ; \&\text{nbsp}; y = - \frac{1}{3}\)

a) Ta có \(A D + D C = A C = A B = 15\) cm và \(\frac{A D}{D C} = \frac{A B}{B C} = \frac{15}{10} = \frac{3}{2}\).

Suy ra \(\left{\right. & A D + D C = 15 \\ & A D = \frac{3}{2} D C\).

Từ đó suy ra \(A D = 9\) cm, \(D C = 6\) cm.

b) Vì \(B D \bot B E\) nên \(B E\) là phân giác ngoài của góc \(B\) của tam giác \(A B C\).

Khi đó ta có \(\frac{A E}{E C} = \frac{A B}{B C}\).

Suy ra \(E C = \frac{A E . B C}{A B} = \frac{A E . 10}{15} = \frac{A E . 2}{3}\).

Suy ra \(3. C E = 2. \left(\right. A C + C E \left.\right)\) hay \(C E = 2. A C\).

Do đó \(C E = 30\) cm.

a) Ta có \(A D + D C = A C = A B = 15\) cm và \(\frac{A D}{D C} = \frac{A B}{B C} = \frac{15}{10} = \frac{3}{2}\).

Suy ra \(\left{\right. & A D + D C = 15 \\ & A D = \frac{3}{2} D C\).

Từ đó suy ra \(A D = 9\) cm, \(D C = 6\) cm.

b) Vì \(B D \bot B E\) nên \(B E\) là phân giác ngoài của góc \(B\) của tam giác \(A B C\).

Khi đó ta có \(\frac{A E}{E C} = \frac{A B}{B C}\).

Suy ra \(E C = \frac{A E . B C}{A B} = \frac{A E . 10}{15} = \frac{A E . 2}{3}\).

Suy ra \(3. C E = 2. \left(\right. A C + C E \left.\right)\) hay \(C E = 2. A C\).

Do đó \(C E = 30\) cm.

ádada

Playing football is my favorite hobby. I started this hobby when I was nine years old. Every afternoon, my friends and I play football at the stadium after stressful school hours. We make two teams and play for about two hour. Football makes me feel happy and energetic. It helps me stay fit and learn how to cooperate with others. In the future, I want to join a real football club and become a good player.