a)
1001<(√n+√(n+1)^2
1001<n+2√(n^2+n) + n+1
1001<2n+1 + 2√(n^2+n)
1000-2n<2√(n^2+n)
500-n<√(n^2+n)
deoarece (n^2+n) nu poate fi patrat perfect ridicam la patrat
250000-1000n+n^2<n^2+n
1001n>250000
4n>4*250000/1001
4n≥1000
cel mai mic 4n este 1000
b)
-1≤x≤1
0≤x+1≤2
x+1=2y
0≤2y≤2
0≤y≤1 (1)
-1≤y-1≤0 (2)
x-1=2y-2
E(x,y)=√[2(x+1)^2 + y^2] + √[2(x-1)^2+(y-1)^2]
E(x,y)=√(2*4y^2 + y^2)+√[2(2y-2)^2 + (y-1)^2]
E(x,y)=√9y^2 + √[9(y-1)^2]
E(x,y)=3|y|+3|y-1| tinem cont de (1) si (2) si obtinem
E(x,y)=3y+3(1-y)
E(x,y)=3
