Question

tìm x biết

a)(4-x)²+15=40

b)(3x-2)¹⁰=(3x-2)⁴

c)x=1+4+4²+...+4²⁰¹⁷

Answer 1

a)(4-x)²+15=40

   (4-x)²=40-15

   (4-x)²=25

    (4-x)²=5²

=>4-x=5

x=5-4

x=1

Answer 2

a) ( 4 - x )² + 15 = 40

( 4 - x )² = 40 - 15

( 4 - x )² = 25

( 4 - x )² = 5²

4 - x = 5

     x = 4 - 5

     x = ( - 1 )

b, ( 3x - 2 )¹⁰ = ( 3x - 2 )⁴

=> x \(\in\left\{0;1\right\}\)

c, X = 1 + 4 + 4² + ......... + 4²⁰¹⁷

4X = 4 + 4¹ + ......... + 4²⁰¹⁸

4X - X = ( 4 + 4¹ + ........ + 4²⁰¹⁸ ) - ( 1 + 4 + 4² + ......... + 4²⁰¹⁷ )

4X - X = 4 + 4¹ + ......... + 4²⁰¹⁸ - 1 - 4 - 4² - ......... - 4²⁰¹⁷

=> 3X = 4²⁰¹⁸ - 1

=> X = \(\frac{4^{2018}-1}{3}\)