\(\dfrac{1}{4}x^2-5xy+25y^2=\left(\dfrac{1}{2}x\right)^2-2.\dfrac{1}{2}x.5y+\left(5y\right)^2\)

\(=\left(\dfrac{1}{2}x-5y\right)^2\)

Bài 1:

a, \(\left(3x-1\right)^3=27=3^3\)

\(\Rightarrow3x-1=3\Rightarrow3x=4\Rightarrow x=\dfrac{4}{3}\)

b, \(2^{x-2}=16=2^{4^{ }}\)

\(\Rightarrow x-2=4\Rightarrow x=6\)

c, \(3^x=9.27=3^2.3^3=3^5\)

\(\Rightarrow x=5\)

d, \(15x-899:29=194\)

\(15x-31=194\Rightarrow15x=225\Rightarrow x=15\)

Bài 2:

a, \(5^2.3^2-32:2^{2^{ }}\)\(=15^2-2^5:2^2=225-8=217\)

b, \(19.37+63.19-400\)\(=19.\left(37+63\right)-400=19.100-100.4=100.\left(19-4\right)\)

\(=100.15=1500\)

c, 205-\(\left\{102-\left[48-\left(16-14\right)^{ }3\right]\right\}\)\(=205-\left\{102-\left[48-2^3\right]\right\}=205-\left(102-40\right)\)

\(=205-62=143\)

CO₂

I was born and raised in Minh Duc, Tu Ky, Hai Duong. Here is the place where I love the best. It is a peaceful place. The air is fresh. The space is quiet. We can enjoy healthy natural conditions without worrying much about environmental pollution. As for social security, my village is a safer place than a city. Morever, people here are friendly and ready to help each other. Most of them live on agriculture and breeding cattle as well as poultry. So the food there are always fresh and tasty. Although I go anywhere, I still think of my village, Minh Duc.

cop trên ta124, mk sẽ áp dụng!!!

16^x=(2⁴)^x=2^4x

128⁴=(2⁷)⁴=2²⁸

theo bài ra ta có:2^4x=2²⁸

suy ra 4x=28 suy ra x=7

nhớ tích nha bạn

\(n^3-1⋮6\)

Ta có: \(n^3-n=n.\left(n^2-1\right)=\left(n-1\right).n.\left(n+1\right)\)

Vì đây là 3 số tự nhiên liên tiếp\(\Rightarrow\left(n-1\right).n.\left(n+1\right)⋮6\)

Vậy \(n^3-1⋮6\)

Dấu hiệu chia hết cho 11 là: Hiệu của tổng các chữ số hàng chắn với tổng các chữ số lẻ chia hết cho 11

\(5^{2x-3}-2.5^2=5^2.3\)

\(5^{2x-3}=5^2.3+2.5^2\)

\(5^{2x-3}=5^2\left(2+3\right)\)

\(5^{2x-3}=5^3\Rightarrow2x-3=3\Rightarrow2x=6\Rightarrow x=3\)