Question

Exercitiul 6
Dau coroana

Answer 1

(2¹+1)(2²+1)(2⁴+1)(2⁸+1)(2¹⁶+1)-2³²=
(2³+2²+2+1)*(2⁴+1)(2⁸+1)(2¹⁶+1)-2³²=
(2⁴-1)/(2-1)*(2⁴+1)(2⁸+1)(2¹⁶+1)-2³²=
(2⁴-1)(2⁴+1)(2⁸+1)(2¹⁶+1)-2³²=
(2⁸-1)(2⁸+1)(2¹⁶+1)-2³²=
(2¹⁶-1)(2¹⁶+1)-2³²=
2³²-1-2³²=-1

Raspuns: -1

Answer 2

Vom folosi formula :

(a-b)(a+b) = a² - b²

[tex]\it (2+1)(2^2+1)(2^4+1)(2^8+1)(2^{16}+1) = \\ \\ = (2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)(2^{16}+1) = \\ \\ (2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^{16}+1) = \\ \\ =(2^4-1)(2^4+1)(2^8+1)(2^{16}+1) = (2^8-1)(2^8+1)(2^{16}+1) = \\ \\ = (2^{16}-1)(2^{16}+1) = 2^{32}-1[/tex]

 Expresia din enunț devine:

$\it 2^{32} -1+2^{32} = -1$