Để: \(\overline{a471}\) chia hết cho 3 thì (\(1\le a\le9\)) 

\(a+4+7+1=a+12\) ⋮ 3

TH1: \(a+12=15\)

\(\Rightarrow a=15-12\)

\(\Rightarrow a=3\)

TH2: \(a+12=18\)

\(\Rightarrow a=18-12\)

\(\Rightarrow a=6\)

TH3: \(a+12=21\)

\(\Rightarrow a=21-12\)

\(\Rightarrow a=9\)

Vậy: \(a\in\left\{3;6;9\right\}\)

Để: \(\overline{5a76}\) chia hết cho 9 thì: \(\left(0\le a\le9\right)\)

\(5+a+7+6=a+18\) ⋮ 9

TH1: \(a+18=18\)

\(\Rightarrow a=18-18\)

\(\Rightarrow a=0\)

TH2: \(a+18=27\)

\(\Rightarrow a=27-18\)

\(\Rightarrow a=9\)

Vậy: \(a\in\left\{0;9\right\}\)

1 + 2 + 3 + ... + n = 300

n.(n + 1) : 2 = 300

n(n + 1) = 300 . 2

n(n + 1) = 600

n² + n - 600 = 0

n² - 24n + 25n - 600 = 0

(n² - 24n) + (25n - 600) = 0

n(n - 24) + 25(n - 24) = 0

(n - 24)(n + 25) = 0

n - 24 = 0 hoặc n + 25 = 0

*) n - 24 = 0

n = 24 (nhận)

*) n + 25 = 0

n = -25 (loại)

Vậy n = 24

n.(n + 1) = 210

n.(n + 1) = 14.15

⇒ n = 14

\(n\cdot\left(n+1\right)=210\)

\(\Rightarrow n\cdot\left(n+1\right)=2\cdot7\cdot3\cdot5\)

\(\Rightarrow n\cdot\left(n+1\right)=14\cdot15\)

\(\Rightarrow n\cdot\left(n+1\right)=14\cdot\left(14+1\right)\)

\(\Rightarrow n=14\)

5²ˣ.5¹⁴ = 5³⁰

5²ˣ = 5³⁰ : 5¹⁴

5²ˣ = 5³⁰⁻¹⁴

5²ˣ = 5¹⁶

2x = 16

x = 16 : 2

x = 8

a) (2x - 1).3⁴ = 3⁷

2x - 1 = 3⁷ : 3⁴

2x - 1 = 3³

2x - 1 = 27

2x = 27 + 1

2x = 28

x = 28 : 2

x = 14

Câu b em ghi đề chính xác lại

Em xem câu b phải vầy không?

2ˣ⁺¹ + 4.2ˣ = 3.2¹²

2ˣ.(2 + 4) = 3.2.2¹¹

2ˣ.6 = 6.2¹¹

2ˣ = 2¹¹

x = 11

\(\left(4x-1\right)^2=25.9\\ \Leftrightarrow\left(4x-1\right)^2=225\\ \Leftrightarrow\left[{}\begin{matrix}\left(4x-1\right)^2=15^2\\\left(4x-1\right)^2=\left(-15\right)^2\end{matrix}\right.\\\Leftrightarrow\left[{}\begin{matrix}4x-1=15\\4x-1=-15\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}4x=16\\4x=-14\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\\x=-\dfrac{7}{2}\end{matrix}\right.\)

(4x-1)^2=(5/3)^2

Suy ra: 4x-1=5/3

4x=5/3+1

4x=8/3

X=8/3:4

X=....

X=51

\(5\left(x+60\right)=980-160\)

\(5\left(x+60\right)=820\)

\(x+60=820:5\)

\(x+60=164\)

\(x=104\)

1

mau lên đi ạ

pls

(x - 1)² + 3² = 5².1¹⁰⁰

(x - 1)² + 9 = 25 .1

(x - 1)² + 9 = 25

(x - 1)² = 25 - 9

(x - 1)² = 16

x - 1 = 4 hoặc x - 1 = -4

*) x - 1 = 4

x = 4 + 1

x = 5

*) x - 1 = -4

x = -4 + 1

x = -3

Vậy x = -3; x = 5

\(\left(x-1\right)^2+3^2=5^2\cdot1^{100}\\ \Leftrightarrow\left(x-1\right)^2+9=25\\ \Leftrightarrow\left(x-1\right)^2=16\\ \Rightarrow\left[{}\begin{matrix}x-1=4\\x-1=-4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5\\x=-3\end{matrix}\right.\)