Tìm \(x:\)\(\left(\frac{21}{x}-2\right)^2-2\left(\frac{21}{x}-2\right)=x+42\)
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a. 52 + (x+3) = 52
=> x + 3 = 52 - 52
=> x + 3 = 0
=> x = -3
b. 23 + (x-32) = 53 - 43
=> 8 + (x-9) = 125 - 64
=> x - 9 = 125 - 64 - 8
=> x - 9 = 53
=> x = 53 + 9
=> x = 62
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\(28\times13+74\times14=14\times2\times13+13\times4\times14=\left(14\times2\times13\right)\left(1+2\right)=1092\)
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Cho mình 1 k nhe ! Cách viết mũ là ấn cái x2 mà bạn nhìn thấy. Cách tắt mũ là ấn lại vào cái đấy
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\(\frac{25}{72}+\frac{25}{90}+\frac{25}{110}+...+\frac{25}{9900}\)
= \(25.\left(\frac{1}{72}+\frac{1}{90}+\frac{1}{110}+...+\frac{1}{9900}\right)\)
= \(25.\left(\frac{1}{8.9}+\frac{1}{9.10}+\frac{1}{10.11}+...+\frac{1}{99.100}\right)\)
= \(25.\left(\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}+...+\frac{1}{99}-\frac{1}{100}\right)\)
= \(25.\left(\frac{1}{8}-\frac{1}{100}\right)\)
= \(25.\frac{23}{200}\)
= \(\frac{23}{8}\)
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18 : 3 + 182 + 3 ( 51 : 17 )
= 6 + 182 + 3 . 3
= 188 + 9
= 197
=))
\(18:3+182+3\left(51:17\right)\)
\(=6+182+3.3\)
\(=6+182+9\)
\(=197\)
Chúc bạn học tốt!
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\(72^{81}=\left(...2^4\right)^{20}\cdot72=...6\cdot...2=...6\)
\(82^{83}=\left(...2^4\right)^{21}:82=\frac{...6}{...2}=...3\)
cảm ơn bạn nhưng cái đề bài không sai đâu, nó là lũy thừa tầng đấy
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B = 1 + 52 + 53 + ... + 52019
5B = 5 + 52 + 53 + ... + 52020
Lấy 5B trừ B theo vế ta có :
5B - B = (5 + 52 + 53 + ... + 52020) - (1 + 52 + 53 + ... + 52019)
4B = 52020 - 1
B = \(\frac{5^{2020}-1}{4}\)
Vậy B = \(\frac{5^{2020}-1}{4}\)
\(B=1+5+5^2+5^3+...+5^{2019}\)
\(\Leftrightarrow5B=5+5^2+5^3+...+5^{2020}\)
\(\Leftrightarrow5B-B=\left(5+5^2+...+5^{2020}\right)-\left(1+5+5^2+...+5^{2019}\right)\)
\(\Leftrightarrow4B=5^{2020}-1\Leftrightarrow B=\frac{5^{2020}-1}{4}\)
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\(\left(\frac{21}{x}-2\right)^2-2\left(\frac{21}{x}-7\right)=x+42\)
\(\Leftrightarrow\frac{441}{x^2}-\frac{126}{x}+8=x+42\)
\(\Leftrightarrow\frac{441}{x^2}-\frac{126}{x}=x+42-8\)
\(\Leftrightarrow\frac{441}{x^2}-\frac{126}{x}=x+34\)
\(\Leftrightarrow\frac{441}{x^2}.x^2-\frac{126}{x}.x^2=x.x^2+34.x^2\)
\(\Leftrightarrow441-126x=x^3+34x^2\)
\(\Leftrightarrow x^3+34x^2=441-126x\)(chuyển vế)
\(\Leftrightarrow x^3+34x^4+126x-441=0\)
\(\Leftrightarrow\left(x+7\right)\left(x^2+27x-63\right)=0\)
\(\Leftrightarrow x+7=0\)
\(\Leftrightarrow x=0-7\)
\(\Leftrightarrow x=-7\)
Vì \(x^2+27-63\ne0\)
=> x = -7
\(\left(\frac{21}{x}-2\right)^2-2\left(\frac{21}{x}-2\right)=x+42\)
\(\Leftrightarrow\frac{441}{x^2}-\frac{126}{x}+8=x+42\)
\(\Leftrightarrow\frac{441}{x^2}-\frac{126}{x}=x+42-8\)
\(\Leftrightarrow\frac{441}{x^2}-\frac{126}{x}=x+34\)
\(\Leftrightarrow\frac{441}{x^2}.x^2-\frac{126}{x}.x^2=x.x^2+34.x^2\)
\(\Leftrightarrow441-126x=x^3+34x^2\)
\(\Leftrightarrow x^3+34x^2=441-126x\)(chuyển vế nhé)
\(\Leftrightarrow x^3+34x^2+126x-441=0\)
\(\Leftrightarrow\left(x+7\right)\left(x^2+27x-63\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x+7=0\\x^3+27x-63\ne0\end{cases}}\Leftrightarrow x=-7\)
=> x = -7