\(\frac{x+6}{15}=\frac{5-x}{7}\Rightarrow7\left(x+6\right)=15\left(5-x\right)\)

\(\Leftrightarrow7x+42=75-15x\Leftrightarrow22x=33\Leftrightarrow x=\frac{3}{2}\)

Ta có :

\(\frac{8}{11}+\frac{a}{b}=\frac{8}{11}.\frac{a}{b}\)

\(\Rightarrow\frac{a}{b}=\frac{8}{11}.\frac{a}{b}-\frac{8}{11}\)

\(\Rightarrow\frac{a}{b}=\frac{8}{11}.\left(\frac{a}{b}-1\right)\)

\(\Rightarrow\frac{a}{b}-1=\frac{8}{11}.\left(\frac{a}{b}-1\right)-1\)

\(\Rightarrow1=\frac{8}{11}.\left(\frac{a}{b}-1\right)-\left(\frac{a}{b}-1\right)\)

\(\Rightarrow\left(\frac{8}{11}-1\right).\left(\frac{a}{b}-1\right)=1\)

\(\Rightarrow\frac{-3}{11}.\left(\frac{a}{b}-1\right)=1\)

\(\Rightarrow\frac{a}{b}-1=1:\frac{-3}{11}=\frac{-11}{3}\)

\(\Rightarrow\frac{a}{b}=\frac{-11}{3}+1=\frac{-8}{3}\)

\(\frac{8}{11}+\frac{a}{b}=\frac{8}{11}.\frac{a}{b}\)

\(\Leftrightarrow\frac{8}{11}+\frac{a}{b}=\frac{8a}{11b}\)

\(\Leftrightarrow\frac{a}{b}-\frac{8a}{11b}=-\frac{8}{11}\)

\(\Leftrightarrow\frac{3a}{11b}=-\frac{8}{11}\)

\(\Leftrightarrow3a=-8b\)

\(\Leftrightarrow\frac{a}{b}=-\frac{8}{3}\)

Sửa đề :

Chứng minh rằng : 4²⁰¹⁰ + 2²⁰¹⁴ ⋮ 10

Bài làm :

Ta có : 4²⁰¹⁰ = 4^2.1005 = (4²)¹⁰⁰⁵ = .......6¹⁰⁰⁵ = ......6

           2²⁰¹⁴ = 2²⁰¹².2² = 2^4.503 . 4 = (2⁴)⁵⁰³ . 4 = .......6⁵⁰³ . 4 = .......6 . 4 = .......4

Khi đó 4²⁰¹⁰ + 2²⁰¹⁴ = ......6 + ......4 = ......0 ⋮ 10

Vậy 4²⁰¹⁰ + 2²⁰¹⁴ ⋮ 10

xin lỗi, mình cứ hay chép sai đề

Chia hết cho 5 nha

Sai đề 

Vì 9^n tận cùng luôn là số lẻ 

2^n luôn là số chẵn 

Nên hiệu luôn là số lẻ 

Đặt \(\frac{x}{-2}=\frac{y}{5}=\frac{z}{-7}=k\Leftrightarrow\hept{\begin{cases}x=-2k\\y=5k\\z=-7k\end{cases}}\)

Khi đó A = \(\frac{-x+3y-z}{2x-7y-3z}=\frac{-\left(-2k\right)+3.5k-\left(-7k\right)}{2\left(-2k\right)-7.5k-3\left(-7k\right)}=\frac{24k}{-18k}=-\frac{4}{3}\)

Đặt \(x=-2k;y=5k;z=-7k\)

\(A=\frac{2k+3.5k+7k}{2.\left(-2k\right)-7.5k-3.\left(-7k\right)}=\frac{24k}{-18k}=-\frac{24}{18}=-\frac{4}{3}\)

\(Q=19-2x-3+13+45\)

\(=-2x+\left(19-3+13+45\right)\)

\(=-2x+74\)

\(Q=19-2x-3+13+45=-2x+74\)