b) 1-2-3+4+5-6-7+8+......+1989-1990-1991+1992+1993

=(1-2-3+4)+(5-6-7+8)+.....+(1989-1990-1991+1992)+1993

=0+0+...+0+1993=1993.

a.\(\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}=\frac{x+1}{13}+\frac{x+1}{14}\Rightarrow\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}-\frac{x+1}{13}-\frac{x+1}{14}=0\)

\(\Rightarrow\left(x+1\right)\left(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\right)=0\)

Mà: \(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\ne0\Rightarrow x+1=0\Rightarrow x=-1\)

b.

\(\frac{x+4}{1990}+\frac{x+3}{1991}=\frac{x+2}{1992}+\frac{x+1}{1993}\Rightarrow2+\frac{x+4}{1990}+\frac{x+3}{1991}=2+\frac{x+2}{1992}+\frac{x+1}{1993}\)

\(\Rightarrow\left(1+\frac{x+4}{1990}\right)+\left(1+\frac{x+3}{1991}\right)=\left(1+\frac{x+2}{1992}\right)+\left(1+\frac{x+1}{1993}\right)\)

\(\Rightarrow\frac{x+1994}{1990}+\frac{x+1994}{1991}=\frac{x+1994}{1992}+\frac{x+1994}{1993}\)

\(\Rightarrow\frac{x+1994}{1990}+\frac{x+1994}{1991}-\frac{x+1994}{1992}-\frac{x+1994}{1993}=0\)

\(\Rightarrow\left(x+1994\right)\left(\frac{1}{1990}+\frac{1}{1991}-\frac{1}{1992}-\frac{1}{1993}\right)=0\)

\(\frac{1}{1990}+\frac{1}{1991}-\frac{1}{1992}-\frac{1}{1993}\ne0\Rightarrow x+1994=0\Rightarrow x=-1994\)

Áp dụng tính chất :

\(\dfrac{a}{b}>1\Leftrightarrow\dfrac{a}{b}>\dfrac{a+m}{b+m}\) ta có :

\(B=\dfrac{10^{1993}+1}{10^{1992}+1}>\dfrac{10^{1993}+1+9}{10^{1992}+1+9}=\dfrac{10^{1993}+10}{10^{1992}+10}=\dfrac{10\left(10^{1992}+1\right)}{10\left(10^{1991}+1\right)}=A\)

\(\Leftrightarrow B>A\)

bọn điên mới chả lời

liên quan đến mày àccon chó kia

a.

\(\left(0,25\right)^3\times32\)

\(=\left(0,25\right)^3\times2^5\)

\(=\left(0,25\right)^3\times2^3\times2^2\) 

\(=\left(0,25\times2\right)^3\times4\)

\(=\left(0,5\right)^3\times4\)

\(=0,125\times4\)

\(=0,5\)

b.

\(\left(-0,125\right)^3\times80^4\)

\(=\left(-0,125\right)^3\times80^3\times80\)

\(=\left(-0,125\times80\right)^3\times80\)

\(=\left(-10\right)^3\times80\)

\(=-1000\times80\)

\(=-80000\)

c.

\(3^{1994}+3^{1993}-3^{1992}\)

\(=3^{1992}\times\left(3^2+3-1\right)\)

\(=3^{1992}\times\left(9+3-1\right)\)

\(=3^{1992}\times11\)

\(\Rightarrow3^{1994}+3^{1993}-3^{1992}⋮11\)

d.

\(4^{13}+32^5-8^8\)

\(=\left(2^2\right)^{13}+\left(2^5\right)^5-\left(2^3\right)^8\)

\(=2^{26}+2^{25}-2^{24}\)

\(=2^{24}\times\left(2^2+2-1\right)\)

\(=2^{24}\times\left(4+2-1\right)\)

\(=2^{24}\times5\)

\(\Rightarrow4^{13}+32^5-8^8⋮5\)

Chúc bạn học tốt

thanhks bạn nhiều 

Bài 2: 

a: \(5^{2008}+5^{2007}+5^{2006}\)

\(=5^{2006}\left(5^2+5+1\right)=5^{2006}\cdot31⋮31\)

b: \(8^8+2^{20}\)

\(=2^{24}+2^{20}\)

\(=2^{20}\left(2^4+1\right)=2^{20}\cdot17⋮17\)