Question

1)Tìm x

(5-x)^3=-64

2)Cho A =4+4^2+4^3+4^4+........+4^99+4^100.Tìm số dư khi chia A cho 5

Answer 1

\(\left(5-x\right)^3=-64\)

\(\Leftrightarrow\left(5-x\right)^3=\left(-4\right)^3\)

\(\Leftrightarrow5-x=-4\)

\(\Leftrightarrow x=9\)

Answer 2

1)

( 5 - x )³ = - 64

( 5 - x )³ = ( - 4 )³

\(\Rightarrow\)5 - x = - 4

x = 5 - ( - 4 )

x = 5 + 4

x = 9

2)

A = 4 + 4² +4³ + 4⁴ + ........ + 4⁹⁹ + 4¹⁰⁰

A = 4(4+1) + 4³(4+1) + 4⁵(4+1) + ........... + 4⁹⁹(4+1)

A = 4 . 5 + 4³ . 5 + 4⁵ . 5 + ............ + 4⁹⁹ . 5

A = 5(4+4³ + 4⁵ + ..........+ 4⁹⁹ )

Mà 5 \(⋮\) 5 \(\Rightarrow\) 5(4+4³ + 4⁵ + ........ + 4⁹⁹ ) \(⋮\) 5

Vậy A chia 5 dư 0