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1+2+3+4+5+6+7+8+9= 45
2+2+2+2+2+2+2+2+2+2= 20
10+20+30+49+50+60+70+80+90= 459
\(\frac{x-96}{2}+\frac{x-88}{4}+\frac{x-76}{6}+\frac{x-60}{8}=14\)
\(\frac{x-96}{2}-2+\frac{x-88}{4}-3+\frac{x-76}{6}-4+\frac{x-60}{8}-5=0\)
\(\frac{x-96}{2}-\frac{4}{2}+\frac{x-88}{4}-\frac{12}{4}+\frac{x-76}{6}-\frac{24}{6}+\frac{x-60}{8}-\frac{40}{8}=0\)
\(\frac{x-96-4}{2}+\frac{x-88-12}{4}+\frac{x-76-24}{6}+\frac{x-60-40}{8}=0\)
\(\frac{x-100}{2}+\frac{x-100}{4}+\frac{x-100}{6}+\frac{x-100}{8}=0\)
\((x-100)\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+\frac{1}{8}\right)=0\)
\(\Rightarrow x-100=0\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+\frac{1}{8}>0\right)\)
\(\Rightarrow x=100\)
a)
\(P=\dfrac{x^{10}-x^8+x^6-x^4+x^2-1}{x^4-1}\)
\(=\dfrac{x^8\left(x^2-1\right)+x^4\left(x^2-1\right)+\left(x^2-1\right)}{\left(x^2-1\right)\left(x^2+1\right)}\)
\(=\dfrac{\left(x^2-1\right)\left(x^8+x^4+1\right)}{\left(x^2-1\right)\left(x^2+1\right)}\)
\(=\dfrac{x^8+x^4+1}{x^2+1}\)
b)
\(Q=\dfrac{x^{40}+x^{30}+x^{20}+x^{10}+1}{x^{45}+x^{40}+x^{35}+...+x^{10}+x^5+1}\)
\(=\dfrac{x^{40}+x^{30}+x^{20}+x^{10}+1}{\left(x^{45}+x^{35}+...+x^5\right)+\left(x^{40}+x^{30}+...+1\right)}\)
\(=\dfrac{x^{40}+x^{30}+x^{20}+x^{10}+1}{x^5\left(x^{40}+x^{30}+...+1\right)+\left(x^{40}+x^{30}+...+1\right)}\)
\(=\dfrac{x^{40}+x^{30}+x^{20}+x^{10}+1}{\left(x^{40}+x^{30}+...+1\right)\left(x^5+1\right)}\)
\(=\dfrac{1}{\left(x^5+1\right)}\)
cái câu b dòng cuối mẫu số đóng mở ngoặc chi cho mệt ei =.=
\(a,\)( sửa lại xíu đề cho đúng nhé )
\(\frac{1}{x-1}-\frac{3x^2}{x^3-1}=-\frac{2x}{x^2+x+1}\)
\(\Rightarrow\frac{x^2+x+1}{\left(x-1\right)\left(x^2+x+1\right)}-\frac{3x^2}{\left(x-1\right)\left(x^2+x+1\right)}=-\frac{2x\left(x-1\right)}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(\Rightarrow x^2+x+1-3x^2=-2x^2+2x\)
\(\Rightarrow x=1\)
\(g,\)\(\left(x+2\right)\left(x+4\right)\left(x+6\right)\left(x+8\right)=-16\)
\(\Rightarrow\left(x^2+10x+16\right)\left(x^2+10x+24\right)=-16\)
Đặt \(x^2+10x+16=a\)
\(\Rightarrow a\left(a+8\right)=-16\)
\(\Rightarrow a^2+8a+16=0\)
\(\Rightarrow\left(a+4\right)^2=0\)
\(\Leftrightarrow\left(x^2+10x+20\right)^2=0\)
\(\Rightarrow x^2+10x+25-25=0\)
\(\Rightarrow\left(x+5\right)^2-\left(\sqrt{5}\right)^2=0\)
\(\Rightarrow\left(x+5-\sqrt{5}\right)\left(x+5+\sqrt{5}\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x=-5+\sqrt{5}\\x=-5-\sqrt{5}\end{cases}}\)
1; 1; 2; 4; 6; 10; 16; 26;..42..; 68.
2; 8; 14; 20; .26....; .32.....
Học tốt!!!!!!!!!
\(\dfrac{1.2}{1^2}.\dfrac{2.3}{2^2}.\dfrac{3.4}{3^2}...\dfrac{9.10}{9^2}.\dfrac{10.11}{10^2}\left(x-2\right)=-20\left(x+1\right)+60\)
\(\Leftrightarrow\dfrac{1.2^2.3^2.4^2...10^2.11}{1^2.2^2.3^2....10^2}\left(x-2\right)+20\left(x+1\right)=60\)
\(\Leftrightarrow11\left(x-2\right)+20\left(x+1\right)=60\)
\(\Leftrightarrow31x=62\)
\(\Rightarrow x=2\)
8 =80