Question

Comparati
a) 2 la 302 si 3 la 203
b) 2 la 87 + 2 la 86 + 2 la 85 si 5 la 35 + 5 la 34

Answer 1

2^302=2^300*2^2=4*(2^3)^100
3^203=3^200*3^3=3^3(3^2)^100
4<3^3
(2^3)^100<(3^2)^100, pt ca 2^3<3^2, 8<9
daca inmultesc rezulta ca 2^302<3^203

b) 2^85*(2^2+2+1)=(2^5)^17*7
    5^34(5+1)=6*(5^2)^17
7>6
(2^5)^17>(5^2)^17 pt ca 2^5>5^2, 32>25
daca inmultesc cele 2 relatii rezulta ca
2^87+2^86+2^85>5^35+5^34