(1+ . 5-√5/1-√5) (5+√5\1+√5. +1) 1/√3-√2+1/√3+√2 Giúp mik vs cảm ơn
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\(\left(\frac{1}{7}x-\frac{2}{7}\right)\left(\frac{1}{5}x+\frac{3}{5}\right)\left(\frac{1}{3}x+\frac{4}{3}\right)=0\)
<=> \(\frac{x-2}{7}.\frac{x+3}{5}.\frac{x+4}{3}=0\)
<=> \(\frac{x-2}{7}=0\)hoặc \(\frac{x+3}{5}=0\); \(\frac{x+4}{3}=0\)
Nếu \(\frac{x-2}{7}=0\)<=> \(x-2=0\)<=> \(x=2\)
Nếu \(\frac{x+3}{5}=0\)<=> \(x+3=0\) <=> \(x=3\)
Nếu \(\frac{x+4}{3}=0\)<=> \(x+4=0\)<=> \(x=4\)
Vây x= 2 hoặc 3; 4
\(B=1+\frac{1}{5}+\frac{1}{5^2}+\frac{1}{5^3}+...+\frac{1}{5^{100}}\)
\(\Rightarrow5B=5+1+\frac{1}{5}+\frac{1}{5^2}+...+\frac{1}{5^{99}}\)
\(\Rightarrow5B-B=5-\frac{1}{5^{100}}\)
\(\Rightarrow B=\frac{5-\frac{1}{5^{100}}}{4}\)
\(B=1+\frac{1}{5}+\frac{1}{5^2}+\frac{1}{5^3}+...+\frac{1}{5^{100}}\)
\(5B=1+5+\frac{1}{5}+\frac{1}{5^2}+...+\frac{1}{5^{99}}\)
\(5B-B=\left(1+5+\frac{1}{5}+...+\frac{1}{5^{99}}\right)-\left(1+\frac{1}{5}+\frac{1}{5^2}+...+\frac{1}{5^{100}}\right)\)
\(4B=5-\frac{1}{5^{100}}\)
\(B=\frac{5-\frac{1}{5^{100}}}{4}\)
hok tốt!!
\(\frac{2}{5}\times\frac{1}{2}-\frac{2}{5}\times\frac{1}{3}-\frac{2}{5}\times\)\(\frac{1}{6}\)
\(=\frac{2}{5}\times\left(\frac{1}{2}-\frac{1}{3}-\frac{1}{6}\right)\)
\(=\frac{2}{5}\times\frac{0}{6}\)
\(=\frac{2}{5}\times0\)
\(=0\)
\(\frac{2}{5}\times\frac{1}{2}-\frac{2}{5}\times\frac{1}{3}-\frac{2}{5}\times\frac{1}{6}\)
\(=\frac{2}{5}\times\left(\frac{1}{2}-\frac{1}{3}-\frac{1}{6}\right)\)
\(=\frac{2}{5}\times0\)
\(=0\)
`a)5/9:(1/11-5/22)+5/9:(1/15-2/3)`
`=5/9:(2/22-5/22)+5/9:(1/15-10/15)`
`=5/9:(-3)/22+5/9:(-9)/15`
`=5/9*(-22)/3+5/9*(-5)/3`
`=5/9*(-22/3+(-5)/3)`
`=5/9*(-9)=-5`
Bài làm
\(4\frac{1}{5}-\left(2\frac{3}{7}+8\frac{1}{5}\right)\)
\(=\frac{21}{5}-\left(\frac{17}{7}+\frac{41}{5}\right)\)
\(=\frac{147}{35}-\left(\frac{85}{35}+\frac{287}{35}\right)\)
\(=\frac{147-85-287}{35}=\frac{-225}{35}=-\frac{45}{7}\)
Đặt \(\left(1+5+5^2+5^3+...+5^{2010}+5^{2011}\right)\) là A
\(\Rightarrow5A=5+5^2+5^3+5^4+...+5^{2011}+5^{2012}\)
\(\Rightarrow5A-A=5+5^2+5^3+5^4+...+5^{2011}+5^{2012}-1-5-5^2-5^3-...-5^{2010}-5^{2011}\)
\(\Rightarrow4A=5^{2012}-1\)
\(\Rightarrow A=\frac{1}{4}\left(5^{2012}-1\right)\)
Thay A vào, ta có:
\(\frac{1}{4}\left(5^{2012}-1\right)\left(x-1\right)=5^{2012}-1\)
\(\frac{1}{4}\left(x-1\right)=1\)
\(x-1=4\)
\(x=3\)
a: \(=\left(1+\dfrac{\sqrt{5}\left(\sqrt{5}-1\right)}{-\left(\sqrt{5}-1\right)}\right)\left(\sqrt{5}+1\right)\)
=(1-căn 5)(1+căn 5)
=1-5=-4
b: \(=\sqrt{3}+\sqrt{2}+\sqrt{3}-\sqrt{2}=2\sqrt{3}\)