Question

Comparati numerele : a=9x2^100- 2^99x5-3x 2^101 si b = 5x 3 ^ 67 - 3 ^ 68 -5 x 3 ^ 66

Answer 1

a=9*2¹⁰⁰ -2⁹⁹ *5 -3*2¹⁰¹= 2⁹⁹*(18- 5 -12)=2⁹⁹*1= 2⁹⁹= (2³)³³= 8³³

b=5*3⁶⁷-3⁶⁸ -5*3⁶⁶= 3⁶⁶*(15- 9-5)= 3⁶⁶*1= 3⁶⁶= (3²)³³= 9³³

a < b

Answer 2

a = 9 × 2^100 - 2^99 × 5 - 3 × 2^101 = 2^99 × ( 9 × 2^1 - 1×5 - 3 × 2) = 2^99 × ( 18 - 11) = 2^99 × 9 = (2^3)^33 × 9 = 8^33 × 9 = 8^33 × (8 +1) ; b = 5 × 3^67 - 3^68 - 5 × 3^66 = 3^66 × ( 5 × 3^1 - 3^2 - 5 × 1) = 3^66 × (15 - 11) = 3^66 × 4 = (3^2)^33 × 4 = 9^33 × 4 = 9^33 × ( 9 - 5) => a> b