1. Determine all pairs of integer (x;y) such that 2xy^2+x+y+1x^2+2y^2+xy 2. Let a,b,c satisfies the conditions hept{begin{cases}5ge age bge cge0a+ble8a+b+c10end{cases}} Prove that 2a^2+b^2+c^2le38 3. Let a nad b satis fy the conditions hept{begin{cases}a^3-6a^2+15a9b^3-3b^2+6b-1end{cases}} Find the value ofleft(a-bright)^{2014} ? 4. Find the smallest positive integer n such that the number 2^n+2^8+2^{11} is a perfect square.
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.
