Question

Comparati nr:
a = 2^87 - 2^86 - 2^85
b = 5^86 - 4 • 5^85
dau coroana plzzzz​

Answer 1

Răspuns: a < b

Explicație pas cu pas:

a = 2⁸⁷ - 2⁸⁶ - 2⁸⁵

a = 2⁸⁵ · (2⁸⁷⁻⁸⁵ - 2⁸⁶⁻⁸⁵ - 2⁸⁵⁻⁸⁵)

a = 2⁸⁵ · (2² - 2¹ - 2⁰)

a = 2⁸⁵ · (2² - 2 - 1)

a = 2⁸⁵ · (4 - 2 - 1)

a = 2⁸⁵ · 1

a = 2⁸⁵ = (2⁵)¹⁷ = 32¹⁷

b = 5⁸⁶ - 4 · 5⁸⁵

b = 5⁸⁵ · (5⁸⁶⁻⁸⁵ - 4 · 5⁸⁵⁻⁸⁵)

b = 5⁸⁵ · (5¹ - 4 · 5⁰)

b = 5⁸⁵ · (5 - 4 · 1)  

b = 5⁸⁵ · 1

b = 5⁸⁵

a < b

Answer 2

$\it \left.\begin{aligned} \it a=2^{85}(2^2-2-1)=2^{85}\\ \\\it b=5^{85}(5-4)=5^{85}\ \ \ \ \ \ \ \end{aligned}\right\} \Rightarrow a<b$