Question

Comparati numerele: 2la puterea 87+2la puterea 86+2la puterea 85 si 5la puterea 35+5la puterea 34.
Va rog urgent dau coroana!

Answer 1

$\text{Faptul ca avem aceeasi baza ne duce cu gandul al factor comun:}\\2^{87}+2^{86}+2^{85}=2^{85}(2^2+2+1)=2^{85}(4+2+1)=7\cdot 2^{85}\\5^{35}+5^{34}=5^{34}(5+1)= 6\cdot 5^{34}\\\text{Ramane sa comparam }7\cdot 2^{85} \text{ si }6\cdot 5^{34}\\7\cdot 2^{85} ~~~~~~ 6\cdot 5^{34}\\7\cdot(2^{5})^{17}~~~~~ 6\cdot (5^2)^{17}\\7\cdot 32^{17}< 6\cdot 25^{17}$

Answer 2

2⁸⁷ + 2⁸⁶ + 2⁸⁵ = 2⁸⁵x ( 2² + 2 + 1 ) =2⁸⁵ x 7

5³⁵ + 5³⁴ = 5³⁴ x ( 5 + 1 ) = 5³⁴ x 6

2⁸⁵ x 7 = ( 2⁵ ) ¹⁷ x 7 = 32¹⁷ x 7

5³⁴ x 6 = ( 5² )¹⁷ x 6 = 25¹⁷ x 6

==>  32¹⁷ x 7  >  25¹⁷ x 6  ==>  2⁸⁵ x 7 >   5³⁴x 6