Question

Comparati numerele a = 3⁷⁹-2 • 9³⁹-2•3⁷⁷-9³⁸ si b=4⁵⁰-2⁹⁹-3•2⁹⁷-8³².​

Answer 1

$a=3^{79}-2*9^{39}-2*3^{77}-9^{38}=\\=3^{79}-2*3^{2*39}-2*3^{77}-3^{2*38}=\\=3^{79}-2*3^{78}-2*3^{77}-3^{76}=\\=3^{76}(3^3-2*3^2-2*3-1})=\\=3^{76}(27-2*9-6-1)=3^{76}(20-18)=3^{76}*2$

$b=4^{50}-2^{99}-3*2^{97}-8^{32}=\\=2^{2*50}-2^{99}-3*2^{97}-2^{3*32}=\\=2^{100}-2^{99}-3*2^{97}-2^{96}=\\=2^{96}(2^4-2^3-3*2-1)=\\=2^{96}(16-8-6-1)=2^{96}*1$

impartim ambele numere cu 2si obtinem:

$a=3^{76}$ si $b=2^{95}$

si a<b

Explicație pas cu pas: