Question

[La Ho Thi Minh Khue]

1) The rectangle has length p and breath q (cm), where p and q are intergers. If p and q satisfy the equation pq+q=13 + q²

then the maxnium area of the rectangle

2) Let a,b and c be positive intergers such that ab + bc=518 and ab-ac=360. Find the largest value of the product abc.

P/s: As you may now, These are some questions from the 8 round of Math Violympic. Plz help me as much as you can! Thanks for all!

Answer 1

[Bình Dị]

Ta có: \(pq+q=13+q^2\Leftrightarrow q\left(p+1\right)=13+q^2\)

Vì\(q^2⋮q\Leftrightarrow13⋮q\Leftrightarrow\left[{}\begin{matrix}q=1\\q=13\end{matrix}\right.\)

Nếu q =1 thì:\(p+1=14\Leftrightarrow p=13\)

\(\Rightarrow pq=13\left(cm^2\right)\)(1)

Nếu q=13 thì:\(13p+13=182\Leftrightarrow p=13\)

\(\Rightarrow pq=169\left(cm^2\right)\)(2)

Từ (1)(2) ta có: \(max\left(pq\right)=169\left(cm^2\right)\)

Bạn xem hộ mình sai ở đâu k

Answer 2

[Bình Dị]

câu 2 thì dựa vào đây nhưng chưa đầy đủ đâu bạn làm nốt nhé https://hoc24.vn/hoi-dap/question/197024.html?pos=675443