1. Determine all pairs of integer (x;y) such that \(2xy^2+x+y+1=x^2+2y^2+xy\) 2. Let a,b,c satisfies the conditions \(\hept{\begin{cases}5\ge a\ge b\ge c\ge0\\a+b\le8\\a+b+c=10\end{cases}}\) Prove that \(2a^2+b^2+c^2\le38\) 3. Let a nad b satis fy the conditions \(\hept{\begin{cases}a^3-6a^2+15a=9\\b^3-3b^2+6b=-1\end{cases}}\) Find the value of\(\left(a-b\right)^{2014}\) ? 4. Find the smallest positive integer n such that the number \(2^n+2^8+2^{11}\) is a perfect...
Đọc tiếp
1. Determine all pairs of integer (x;y) such that \(2xy^2+x+y+1=x^2+2y^2+xy\)
2. Let a,b,c satisfies the conditions
\(\hept{\begin{cases}5\ge a\ge b\ge c\ge0\\a+b\le8\\a+b+c=10\end{cases}}\)
Prove that \(2a^2+b^2+c^2\le38\)
3. Let a nad b satis fy the conditions
\(\hept{\begin{cases}a^3-6a^2+15a=9\\b^3-3b^2+6b=-1\end{cases}}\)
Find the value of\(\left(a-b\right)^{2014}\) ?
4. Find the smallest positive integer n such that the number \(2^n+2^8+2^{11}\) is a perfect square.
