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\(\left(\dfrac{1}{2}+1\right)\times\left(\dfrac{1}{3}+1\right)\times\left(\dfrac{1}{4}+1\right)\times\left(\dfrac{1}{5}+1\right)\times\left(\dfrac{1}{6}+1\right)\)
\(=\dfrac{3}{2}\times\dfrac{4}{3}\times\dfrac{5}{4}\times\dfrac{6}{5}\times\dfrac{7}{6}\)
\(=\dfrac{3\times4\times5\times6\times7}{2\times3\times4\times5\times6}\)
\(=\dfrac{7}{2}\)
(
2
1
+1)×(
3
1
+1)×(
4
1
+1)×(
5
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+1)×(
6
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+1)
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3
2
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4
3
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5
4
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6
5
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7
6
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2
3
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3
4
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4
5
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5
6
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2×3×4×5×6
3×4×5×6×7
=
7
2
=
2
7
\(\dfrac{a}{27}-\dfrac{2}{9}=\dfrac{6}{18}\)
\(\dfrac{a}{27}=\dfrac{6}{18}+\dfrac{2}{9}\)
\(\dfrac{a}{27}=\dfrac{5}{9}\)
\(\dfrac{a}{27}=\dfrac{15}{27}\)
=> \(a=15\)
\(\dfrac{y}{20}-\dfrac{7}{12}=\dfrac{11}{30}\)
\(\dfrac{y}{20}=\dfrac{11}{30}+\dfrac{7}{12}\)
\(\dfrac{y}{20}=\dfrac{19}{20}\)
\(y\times20=19\times20\)
\(y\times20=380\)
\(y=19\)
\(\dfrac{y}{20}-\dfrac{7}{12}=\dfrac{11}{30}\)
\(\dfrac{y}{20}=\dfrac{11}{30}+\dfrac{7}{12}\)
\(\dfrac{y}{20}=\dfrac{22}{60}+\dfrac{35}{60}\)
\(\dfrac{y}{20}=\dfrac{57}{60}\)
\(y=\dfrac{57}{60}\times20\)
\(y=\dfrac{57}{3}\)
y =19
a \(\dfrac{3}{8}\times\dfrac{5}{2}+\dfrac{5}{8}\times\dfrac{5}{2}=\dfrac{5}{2}\left(\dfrac{3}{5}+\dfrac{5}{8}\right)=\dfrac{5}{2}\times\dfrac{8}{8}=\dfrac{5}{2}\times1=\dfrac{5}{2}\)
b \(33.12\times0=0\)
\(0=\left(x-5\right)^5-\left(x-5\right)^4\)
\(\left(x-5\right)^4\left(x-5-1\right)=0\)
\(\orbr{\begin{cases}\left(x-5\right)^4=0\\x-6=0\end{cases}}\)
\(\orbr{\begin{cases}x=5\\x=6\end{cases}}\)
a,
\(2^x=32\)
\(2^x=2^5\)
\(\Rightarrow x=5\)
b,
2x = 124
x = 62
c,
\(x^{15}-x=0\)
\(x\left(x^{14}-1\right)=0\)
\(\orbr{\begin{cases}x=0\\x^{14}-1=0\end{cases}}\)
\(\orbr{\begin{cases}x=0\\x=\pm1\end{cases}}\)
a)\(2^x.4=128\Leftrightarrow2^x=32\Leftrightarrow2^x=2^5\Rightarrow x=5\)
b)\(\left(2x+1\right)=125\Leftrightarrow2x=126\Leftrightarrow x=13\)
c)\(x^{15}=x\Leftrightarrow\orbr{\begin{cases}x=\pm1\\x=0\end{cases}}\)
d) \(\left(x-5\right)^4=\left(x-5\right)^5\Leftrightarrow\orbr{\begin{cases}x-5=1\\x-5=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=6\\x=5\end{cases}}\)
a,
\(2^x=32\)
\(2^x=2^5\)
\(\Rightarrow x=5\)
b,
2x = 124
x = 62
c,
\(x^{15}-x=0\)
\(x\left(x^{14}-1\right)=0\)
\(\orbr{\begin{cases}x=0\\x^{14}-1=0\end{cases}}\)
\(\orbr{\begin{cases}x=0\\x^{14}=1\end{cases}}\)
\(\orbr{\begin{cases}x=0\\x=\pm1\end{cases}}\)
d,
\(0=\left(x-5\right)^5-\left(x-5\right)^4\)
\(\left(x-5\right)^4\left(x-5-1\right)=0\)
\(\orbr{\begin{cases}\left(x-5\right)^4=0\\x-6=0\end{cases}}\)
\(\orbr{\begin{cases}x=5\\x=6\end{cases}}\)
\(a\times2+a:2=5\)
\(a\times2+a\times\dfrac{1}{2}=5\)
\(a\times\left(2+\dfrac{1}{2}\right)=5\)
\(a\times\dfrac{5}{2}=5\)
\(a=5:\dfrac{5}{2}\)
\(a=2\)
Vậy \(a=2\)
\(2,25-\left(5\times a-125:5\right)=0\)
\(2,25-5\times a+25=0\)
\(27,25-5\times a=0\)
\(5\times a=27,25\)
\(a=27,25:5\)
\(a=5,45\)
Vậy a=5,45