Question

Comparati numerele: 2 la 87 plus 2 la 86 plus 2 la 85 cu 5 la 35 plus 5 la 34

rapid dau 80 puncte​

Answer 1

Răspuns:

2⁸⁷+2⁸⁶+2⁸⁵=2⁸⁵(2²+2+1)=2⁸⁵×7=(2⁵)¹⁷×7= 32¹⁷×7

5³⁵+5³⁴=5³⁴(5+1)=5³⁴×6=(5²)¹⁷×6= 25¹⁷×6

2⁸⁷+2⁸⁶+2⁸⁵ > 5³⁵+5³⁴

Answer 2

2⁸⁷ + 2⁸⁶ + 2⁸⁵ = 2⁸⁵ x (2²+2¹+1) = 2⁸⁵ x 7

5³⁵ + 5³⁴ = 5³⁴ x (5¹+1) = 5³⁴ x 6

Ducem puterile la acelasi exponent pt a compara mai usor

2⁸⁵ = 2⁵ x 2¹⁷ = (2⁵)¹⁷ = 32¹⁷

5³⁴ = 5² x 5¹⁷ = (5²)¹⁷ = 25¹⁷

În acest caz 32¹⁷x7 > 25¹⁷x6

2⁸⁷ + 2⁸⁶ + 2⁸⁵ > 5³⁵ + 5³⁴