Question

Compară puterile: 2^87 + 2^86 +2^85 cu 5^35 +5^34. ​

Answer 1

Răspuns:

2⁸⁷ + 2⁸⁶ + 2⁸⁵  >  5³⁵ + 5³⁴

Explicație pas cu pas:

2⁸⁷ + 2⁸⁶ + 2⁸⁵ = 2⁸⁵ × (2² + 2 + 1) = 2⁸⁵ × (4 + 2 +1) = 2⁸⁵ × 7

5³⁵ + 5³⁴ = 5³⁴ × (5 + 1) = 5³⁴ × 6

2⁸⁵ × 7 =  2⁵ˣ¹⁷ × 7 = (2⁵)¹⁷ × 7 = 32¹⁷ × 7

5³⁴ × 6 = 5²ˣ¹⁷ × 6 = (5²)¹⁷ × 6 = 25¹⁷ × 6

32  >  25  si   7  >  6

32¹⁷ × 7  >  25¹⁷ × 6

32 = 2⁵

25 = 5²

2⁸⁵ × 7  >  5³⁴ × 6

2⁸⁷ + 2⁸⁶ + 2⁸⁵  >  5³⁵ + 5³⁴