Question

Să se compare :
A) a=2^123 cu b=5^61×2;
B) a=5^36-2×5^35 cu b=2^85+2^86+2^87+2^88. NU, direct cu explicații!

Answer 1

A) a=2^123=(2^2)^61 × 2 =4^61× 2 =
     b=5^61×2
       5>4
deci b>a


B) a=5^36-2×5^35 =5^35×(5^1-2)=5^35 × 3 = 5^34 × 15 =(5^2)^17 × 15 =25^14×15
b=2^85+2^86+2^87+2^88 =2^85×(2^0+2^1+2^2+2^3)=2^85×(1+2+4+8)=
=2^85×15=(2^5)^17×15= 32^17×15
       32>25
deci b>a