Sk hay quá cô ạ!

Em đăng kí nộp bài qua olm chat ạ!

Em đăng kí tham gia sự kiện "Đánh Thức Tài Năng Nhí"

\(\boxed{\star19/08/2004}\)

Đặt \(B=3^{n+2}-2^{n+2}+3^{n}-2^{n}\)

\(=\left(3^3\cdot3^2+3^{n}\right)-\left(2^{n}\cdot2^2+2^{n}\right)\)

\(=3^{n}\left(9+1\right)-2^{n}\left(4+1\right)\)

\(=3^{n}\cdot10-2^{n}\cdot5\)

\(=3^{n}\cdot10-2^{n-1}\cdot10\)

\(=10\left(3^{n}-2^{n-1}\right)\)

Mà 10 ⋮ 10 nên B ⋮ 10

\(\boxed{\star19/08/2004}\)

Ta có:

\(\widehat{xOy}+\widehat{yOm}=180\degree\) (hai góc kề bù)

\(\Rightarrow\widehat{yOm}=180\degree-\widehat{xOy}\)

\(\Rightarrow\widehat{yOm}=180\degree-60\degree\)

\(\Rightarrow\widehat{yOm}=120\degree\)

Vậy \(\widehat{yOm}=120\degree\)

\(\boxed{\star19/08/2004}\)

\(30-2x^2=12\)

\(\Rightarrow2x^2=18\)

\(\Rightarrow x^2=9\)

\(\Rightarrow\left[\begin{array}{l}x=3\\ x=-3\end{array}\right.\)

Vậy \(x\in\left\lbrace3;-3\right\rbrace\)

ABCD là hình thang cân nên AB//CD

=> \(\widehat{A}=\widehat{B}\) (hai góc kề một đáy bằng nhau)

=> \(\widehat{C}=\widehat{D}\) (hai góc kề một đáy bằng nhau)

=> \(\widehat{A}+\widehat{D}=180\degree\) (hai góc bù nhau)

Mà \(\widehat{A}=3\widehat{D}\)

\(\Rightarrow3\widehat{D}+\widehat{D}=180\degree\)

\(\Rightarrow4\widehat{D}=180\degree\)

\(\Rightarrow\widehat{D}=45\degree\)

\(\Rightarrow\widehat{C}=\widehat{D}=45\degree\)

\(\Rightarrow\widehat{A}=\widehat{B}=3\cdot45\degree=135\degree\)

\(\boxed{\star19/08/2004}\)

Ta có hpt:

\(\begin{cases}\dfrac{1}{x}-\dfrac{1}{y}=15\left(1\right)\\ \dfrac{1}{x}+\dfrac{1}{y}=3\left(2\right)\end{cases}\) (ĐKXĐ: \(x,y\ne0\))

Lấy (1) + (2):

\(\left(\dfrac{1}{x}-\dfrac{1}{y}\right)+\left(\dfrac{1}{x}+\dfrac{1}{y}\right)=15+3\)

\(\Rightarrow\dfrac{1}{x}-\dfrac{1}{y}+\dfrac{1}{x}+\dfrac{1}{y}=18\)

\(\Rightarrow\left(\dfrac{1}{x}+\dfrac{1}{x}\right)+\left(-\dfrac{1}{y}+\dfrac{1}{y}\right)=18\)

\(\Rightarrow\dfrac{2}{x}=18\)

\(\Rightarrow\dfrac{1}{x}=9\)

\(\Rightarrow x=\dfrac19\)

Thay \(x=\dfrac19\) vào (2):

\(9+\dfrac{1}{y}=3\)

\(\Rightarrow\dfrac{1}{y}=-6\)

\(\Rightarrow y=-\dfrac16\)

Vậy hpt có nghiệm duy nhất là \(\left(x;y\right)=\left(\dfrac19;-\dfrac16\right)\)

\(\boxed{\star19/08/2004}\)

45 : 9 - 3 x 0,5 + 5,6

= 5 - 1,5 + 5,6

= 3,5 + 5,6

= 9,1