\(3-x-8=7+3^2\)

\(-5-x=7+9\)

\(-5-x=16\)

\(x=-5-16=-21\)

Vậy \(x=-21\)

đúng

2

\(A=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+\cdots+\frac{1}{n^2}\)

Mà: \(\frac{1}{2^2}<\frac{1}{1\cdot2};\frac{1}{3^2}<\frac{1}{2\cdot3};\ldots;\frac{1}{n^2}<\frac{1}{\left(n-1\right)n}\)

Nên \(A<\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\cdots+\frac{1}{\left(n-1\right)\cdot n}\)

\(A<\frac11-\frac12+\frac12-\frac13+\cdots+\frac{1}{n-1}+\frac{1}{n}\)

\(A<\frac11-\frac{1}{n}\)

Suy ra \(A<1\) (nếu n>1)

\(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}\)

\(=\frac12-\frac13+\frac13-\frac14+\frac14-\frac15+\frac15-\frac16\)

\(=\frac12-\frac16\)

\(=\frac13\)

a) Các đơn thức đồng dạng với nhau là: \(A=3x^2y\) ;\(B=-5x^2y\)

b) Tổng các đơn thức đồng dạng vừa tìm được là:

\(A+B=3x^2y+\left(-5x^2y\right)=\left(3-5\right)x^2y=-2x^2y\)

125; 216; 343; 512; 729

\(3^{x-5}=27\)

\(3^{x-5}=3^3\)

\(x-5=3\)

\(x=3+5=8\)

Vậy \(x=8\)

\(4+2\cdot\left\lbrack3^2-2\cdot\left(5^2-20\right)\right\rbrack+2025^0\)

\(=4+2\cdot\left\lbrack9-2\cdot\left(25-20\right)\right\rbrack+1\)

\(=4+2\cdot\left\lbrack9-2\cdot5\right\rbrack+1\)

=\(4+2\cdot\left\lbrack9-10\right\rbrack+1\)

\(=4+2\cdot\left(-1\right)+1=4-2+1=3\)

Lỗi sai: homeworks

Sửa: I usually do my homework after dinner.