Question

$2^{x} + 2^{y} + 2^{z} = 2336\\x \ \textless \ y \ \textless \ z$

Answer 1

Răspuns:

Explicație pas cu pas:

2^x+2^y + 2^z = 2336 ; x < y < z

2336 = 2⁵·73 = 2⁴·146

146 = 128 + 2 + 16 = 2⁷ + 2¹ + 2⁴ =>

2336 = 2⁴·(2⁷+2¹+2⁴) = 2⁴⁺⁷ + 2⁴⁺¹ + 2⁴⁺⁴ =>

2336 = 2¹¹ + 2⁵ + 2⁸ = 2⁵ + 2⁸ + 2¹¹ =>

x = 5 ; y = 8 ; z = 11

5 < 8 < 11