Задача 55652 ...

5f8854b50fdfb21243667c8c

18.11.2020 11:27:42

Решите неравенство 5 ∙ 3^x + 10^x > 2 ∙ 3^(x+1) + 10^(x-1) + 3^(x+2).

5f3ea7e3faf909182968ddd9

18.11.2020 15:52:51

★

[m]5\cdot 3^{x}+10^{x} > 2\cdot 3^{x+1}+10^{x-1}+3^{x+2}[/m]

[m]10^{x}-10^{x-1} > 2\cdot 3^{x+1}+3^{x+2}-5\cdot 3^{x}[/m]

[m]10^{x-1}\cdot (10-1) > 3^{x}\cdot (2\cdot 3+3^{2}-5)[/m]

[m]10^{x-1}\cdot 9 > 3^{x}\cdot 10[/m]

[m]10^{x-2} > 3^{x-2}[/m]

[m](\frac{10}{3})^{x-2} > 1[/m]

x-2 >0

x>2 - о т в е т