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a)\(\frac{4}{x}=\frac{10}{25}\Rightarrow10x=25\cdot4\)
\(\Rightarrow10x=100\)
\(\Rightarrow x=10\)
b)\(\left|x+\frac{1}{2}\right|-1=\frac{1}{4}\)
\(\Rightarrow\left|x+\frac{1}{2}\right|=\frac{5}{4}\)
\(\Rightarrow x+\frac{1}{2}=\frac{5}{4}\)hoặc\(-\frac{5}{4}\)
Xét \(x+\frac{1}{2}=\frac{5}{4}\)
\(\Rightarrow x=\frac{3}{4}\)
Xét \(x+\frac{1}{2}=-\frac{5}{4}\)
\(\Rightarrow x=-\frac{7}{4}\)
1..a . 4/x=10/25 b. /x+1/2/-1=1/4
4*25=10 /x+1/2/ =1/4+1
100=10x /x+1/2/ =5/4
x=10 <=>x+1/2 =5/4
hoặc =-5/4
<=> x =3/4
Hoặc =-7/4
Câu 2: Ta có \(S=6^2+18^2+30^2+...+126^2\)
\(S=6^2\left(1^2+3^2+5^2+...+21^2\right)\)
\(=6^2.1771=36.1771=63756\)
\(2+\frac{1}{1+\frac{1}{2}}\)
=2+\(\frac{1}{\frac{3}{2}}\)
=2+1:3/2
=2+2/3
=8/3
b. bn viet de sao ma mk chang hieu
a) \(2+\frac{1}{1+\frac{1}{2}}=2+\frac{1}{\frac{3}{2}}=2+\frac{2}{3}=\frac{8}{3}\)
b) \(2+\frac{1}{1+\frac{1}{2+\frac{1}{1+\frac{1}{2}}}}\)
\(=2+\frac{1}{1+\frac{1}{2+\frac{1}{\frac{3}{2}}}}\)
\(=2+\frac{1}{1+\frac{1}{2+\frac{2}{3}}}\)
\(=2+\frac{1}{1+\frac{1}{\frac{8}{3}}}\)
\(=2+\frac{1}{1+\frac{3}{8}}\)
\(=2+\frac{1}{\frac{11}{8}}\)
\(=2+\frac{8}{11}\)
\(=\frac{30}{11}\)
\(\frac{437^2-363^2}{537^2-463^2}\)
\(=\frac{\left(437-363\right)\left(437+363\right)}{\left(537-463\right)\left(537+463\right)}\)
\(=\frac{74.800}{74.1000}\)
\(=\frac{80}{1000}=\frac{2}{25}\)
\(\frac{437^2-363^2}{537^2-463^2}\)
\(=\frac{\left(437-363\right)\left(437+363\right)}{\left(537-463\right)\left(537+463\right)}\)( Áp dụng hằng đẳng thức \(A^2-B^2=\left(A-B\right)\left(A+B\right)\))
\(=\frac{74\cdot800}{74\cdot1000}\)
\(=\frac{4}{5}\)