Question

1.Tìm x y

3 mũ (x -1) + 5 x 3 mũ (x - 1) = 162

2.Rút gọn B = 3 mũ 100 - 3 mũ 99 + 3 mũ 98 - 3 mũ 97 + .... + 3 mũ 2 - 3 + 1

Answer 1

1/ 3^x-1 + 5.3^x-1 = 162

3^x-1(1 + 5) = 162

3^x-1 = \(\frac{162}{6}\)

3^x-1 = 27

3^x-1 = 3³

x - 1 = 3

x = 4

2/ B = 3¹⁰⁰ - 3⁹⁹ + 3⁹⁸ - 3⁹⁷ + ... + 3² - 3 + 1

\(\Rightarrow\) 3B = 3.3¹⁰⁰ - 3.3⁹⁹ + 3.3⁹⁸ - 3.3⁹⁷ + ... + 3.3² - 3.3 + 3.1

= 3¹⁰¹ - 3¹⁰⁰ + 3⁹⁹ - 3⁹⁸ + ... + 3³ - 3² + 3

Ta có:

4B = 3B + B = (3¹⁰¹ - 3¹⁰⁰ + 3⁹⁹ - 3⁹⁸ + ... + 3³ - 3² + 3) + (3¹⁰⁰ - 3⁹⁹ + 3⁹⁸ - 3⁹⁷ + ... + 3² - 3 + 1)

= 3¹⁰¹ + 3¹⁰⁰ - 3¹⁰⁰ + 3⁹⁹ - 3⁹⁹ + 3⁹⁸ - 3⁹⁸ + ... + 3 - 3 + 1

= 3¹⁰¹ + 1

\(\Rightarrow\) B = \(\frac{3^{101}+1}{4}\)