Bài 1: Rút gọn
B=/x-2/+/x-3/-2/x-4/
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Áp dụng tính chất dãy tỉ số bằng nhau ta có :
\(\frac{x}{2}=\frac{y}{4}=\frac{x^4+y^4}{16+256}=\frac{16}{272}=\frac{1}{17}\)
\(\Rightarrow x=\frac{2}{17};y=\frac{4}{17}\)
Ta có \(\frac{a}{b+c}=\frac{b}{c+a}=\frac{c}{a+b}=\frac{a+b+c}{b+c+c+a+a+b}=\frac{a+b+c}{2\left(a+b+c\right)}=\frac{1}{2}\)
=> b + c = 2a ; c + a = 2b ; a + b = 2c
Khi đó P = \(\frac{a+b}{c}+\frac{b+c}{a}+\frac{c+a}{b}=\frac{2c}{c}+\frac{2a}{a}+\frac{2b}{b}=2+2+2=6\)
\(\frac{1}{2}-\frac{1}{3.7}-\frac{1}{7.11}-...-\frac{1}{23.27}\)
\(=\frac{1}{2}-\left(\frac{1}{3.7}+\frac{1}{7.11}+...+\frac{1}{23.27}\right)\)
\(=\frac{1}{2}-\frac{1}{4}.\left(\frac{4}{3.7}+\frac{4}{7.11}+...+\frac{4}{23.27}\right)\)
\(=\frac{1}{2}-\frac{1}{4}.\left(\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+...+\frac{1}{23}-\frac{1}{27}\right)\)
\(=\frac{1}{2}-\frac{1}{4}.\left(\frac{1}{3}-\frac{1}{27}\right)\)
\(=\frac{1}{2}-\frac{1}{4}.\frac{8}{27}\)
\(=\frac{1}{2}-\frac{2}{27}\)
\(=\frac{23}{54}\)
a, \(A=\frac{0,375-0,3+\frac{3}{11}+\frac{3}{12}}{0,625-0,5+\frac{5}{11}+\frac{5}{12}}=\frac{\frac{3}{8}-\frac{3}{10}+\frac{3}{11}+\frac{3}{12}}{\frac{5}{8}-\frac{5}{10}+\frac{5}{11}+\frac{5}{12}}=\frac{3}{5}\)
b, \(2^{17}+2^{14}=2^{17}\left(2^3+1\right)=9.2^{17}⋮9\)( đpcm )
a) A=\(\frac{0,375-0,3+\frac{3}{11}+\frac{3}{12}}{0,625-0,5+\frac{5}{11}+\frac{5}{12}}\)
A=\(\frac{\frac{3}{10}-\frac{3}{10}+\frac{36}{132}+\frac{33}{132}}{\frac{5}{10}-\frac{5}{10}+\frac{60}{132}+\frac{55}{132}}\)
A=\(\frac{69}{132}\):\(\frac{115}{132}\)
A=\(\frac{69}{115}\)
b) 217+214 chia hết cho 9
Ta có :\(2^{17}\)+\(2^{14}\)
=>\(2^3\)+\(2^{14}\)+\(2^{14}\)
=>\(2^{14}\).(8+1)
=>\(2^{14}\).9
Vì 9 chia hết cho 9 nên \(2^{14}\).9 chia hết cho 9
Vậy \(2^{17}\)+\(2^{14}\) chia hết cho 9