Đặt \(A=12.\left(5^2+1\right).\left(5^4+1\right).\left(5^8+1\right).\left(5^{16}+1\right)\)

\(\Rightarrow2A=24.\left(5^2+1\right).\left(5^4+1\right).\left(5^8+1\right).\left(5^{16}+1\right)\)

     \(2A=\left(5^2-1\right).\left(5^2+1\right).\left(5^4+1\right).\left(5^8+1\right).\left(5^{16}+1\right)\)

     \(2A=\left(5^4-1\right).\left(5^4+1\right).\left(5^8+1\right).\left(5^{16}+1\right)\)

     \(2A=\left(5^8-1\right).\left(5^8+1\right).\left(5^{16}+1\right)\)

     \(2A=\left(5^{16}-1\right).\left(5^{16}+1\right)\)

     \(2A=\left(5^{16}\right)^2-1^2\)

     \(2A=5^{32}-1\)

\(\Rightarrow A=\frac{5^{32}-1}{2}.\)

cách giải bài này như nào: 5/20+1/4+6/24+8/32=bao nhiêu

    \(\dfrac{4}{5}\) : (\(\dfrac{4}{5}\) .- \(\dfrac{5}{4}\)) : (\(\dfrac{16}{25}\) - \(\dfrac{1}{5}\))

=  \(\dfrac{4}{5}\) : (-1) : (\(\dfrac{16}{25}\) - \(\dfrac{5}{25}\))

= -\(\dfrac{4}{5}\)  : \(\dfrac{11}{25}\)

= - \(\dfrac{4}{5}\) x \(\dfrac{25}{11}\)

=  - \(\dfrac{20}{11}\)

    \(\dfrac{11}{12}\) : (\(\dfrac{7}{9}\) + \(\dfrac{-1}{3}\)) - (\(\dfrac{2}{3}\) - \(\dfrac{5}{15}\))

= \(\dfrac{11}{12}\) : (\(\dfrac{7}{9}\) - \(\dfrac{3}{9}\)) - (\(\dfrac{2}{3}\) - \(\dfrac{1}{3}\))

= \(\dfrac{11}{12}\) : \(\dfrac{4}{9}\) - \(\dfrac{1}{3}\)

= \(\dfrac{11}{12}\) x \(\dfrac{9}{4}\) - \(\dfrac{1}{3}\)

= \(\dfrac{99}{48}\) - \(\dfrac{1}{3}\)

= \(\dfrac{99}{48}\) - \(\dfrac{16}{48}\)

= \(\dfrac{83}{48}\)  

\(\dfrac{4}{5}\): (\(\dfrac{4}{5}\).-\(\dfrac{5}{4}\)) : (\(\dfrac{16}{25}\) - \(\dfrac{1}{5}\))

=\(\dfrac{4}{5}\) x - 1: (\(\dfrac{16}{25}\) - \(\dfrac{5}{25}\))

= - \(\dfrac{4}{5}\) : \(\dfrac{11}{25}\)

= - \(\dfrac{4}{5}\) x \(\dfrac{25}{11}\)

= - \(\dfrac{20}{11}\) 

\(\dfrac{11}{12}\): (\(\dfrac{7}{9}\) + - \(\dfrac{1}{3}\)) - (\(\dfrac{2}{3}\) - \(\dfrac{5}{15}\))

= \(\dfrac{11}{12}\) : (\(\dfrac{7}{9}\) - \(\dfrac{3}{9}\)) - (\(\dfrac{2}{3}\) - \(\dfrac{1}{3}\))

= \(\dfrac{11}{12}\) : \(\dfrac{4}{9}\) - \(\dfrac{1}{3}\)

= \(\dfrac{11}{12}\) x \(\dfrac{9}{4}\) - \(\dfrac{1}{3}\)

= \(\dfrac{99}{48}\) - \(\dfrac{16}{48}\)

= \(\dfrac{83}{48}\) 

- \(\dfrac{2}{5}\).(\(\dfrac{9}{8}\) + \(\dfrac{16}{32}\) - \(\dfrac{3}{4}\)) - \(\dfrac{9}{10}\)

= - \(\dfrac{2}{5}\).(\(\dfrac{9}{8}\) + \(\dfrac{4}{8}\) - \(\dfrac{6}{8}\)) - \(\dfrac{9}{10}\)

= - \(\dfrac{2}{5}\).(\(\dfrac{13}{8}\) - \(\dfrac{6}{8}\)) - \(\dfrac{9}{10}\)

= - \(\dfrac{2}{5}\).\(\dfrac{7}{8}\) - \(\dfrac{9}{10}\)

= - \(\dfrac{7}{20}\) - \(\dfrac{18}{20}\)

= - \(\dfrac{5}{4}\)

12 . (5^2 + 1) . (5^4 +1) . (5^8 +1) . (5^16 + 1)=24:2(5^2 + 1) . (5^4 +1) . (5^8 +1) . (5^16 + 1)

=(5²-1)(5²+1)(5⁴+1)(5⁸+1)(5¹⁶+1):2

=(5⁴-1)(5⁴+1)(5⁸+1)(5¹⁶+1):2

=(5⁸-1)(5⁸+1)(5¹⁶+1):2

=(5¹⁶-1)(5¹⁶+1):2

=(5³²-1):2

có trong câu hỏi tương tự đấy bạn

\(1+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}\)

\(=\dfrac{5}{4}+\dfrac{1}{8}+\dfrac{1}{16}\)

\(=\dfrac{11}{8}+\dfrac{1}{16}\)

\(=\dfrac{23}{16}\)

______

\(2-\dfrac{1}{8}-\dfrac{1}{12}-\dfrac{1}{16}\)

\(=\dfrac{15}{8}-\dfrac{1}{12}-\dfrac{1}{16}\)

\(=\dfrac{43}{24}-\dfrac{1}{16}\)

\(=\dfrac{83}{48}\)

_________

\(\dfrac{4}{99}\times\dfrac{18}{5}:\dfrac{12}{11}+\dfrac{3}{5}\)

\(=\dfrac{8}{55}:\dfrac{12}{11}+\dfrac{3}{5}\)

\(=\dfrac{8}{55}\times\dfrac{11}{12}+\dfrac{3}{5}\)

\(=\dfrac{2}{15}+\dfrac{3}{5}\)

\(=\dfrac{11}{15}\)

__________

\(\left(1-\dfrac{3}{4}\right)\times\left(1+\dfrac{1}{3}\right)\times\left(1-\dfrac{1}{3}\right)\)

\(=\dfrac{1}{4}\times\dfrac{4}{3}\times\dfrac{2}{3}\)

\(=\dfrac{4\times2}{4\times3\times3}\)

\(=\dfrac{2}{3\times3}\)

\(=\dfrac{2}{9}\)

\(C=12\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)

\(=\frac{1}{2}\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)

\(=\frac{1}{2}\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)

\(=\frac{1}{2}\left(5^8-1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)

\(=\frac{1}{2}\left(5^{16}-1\right)\left(5^{16}+1\right)\)

\(=\frac{1}{2}\left(5^{32}-1\right)\)

\(=\frac{5^{32}-1}{2}\)

Đinh Đức Hùng lấy 5² -1 ở đâu đấy

Lấy xong rồi thì phải chia lại chứ

P= 12.(5²+1)(5⁴ +1)(5⁸+1)(5¹⁶+1) 

=>2P=24.(5²+1)(5⁴ +1)(5⁸+1)(5¹⁶+1) 

=(5² -1)(5²+1)(5⁴+1)(5⁸+1)(5¹⁶+1) 

=(5⁸- 1)(5⁸+1)(5¹⁶+1) 

=(5¹⁶ -1)(5¹⁶ -1) 

= 5³² -1 

\(P=12\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)

\(=\dfrac{\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)}{2}\)

\(=\dfrac{\left(5^8-1\right)\left(5^8+1\right)\left(5^{16}+1\right)}{2}\)

\(=\dfrac{\left(5^{16}-1\right)\left(5^{16}+1\right)}{2}\)

\(=\dfrac{5^{32}-1}{2}\)

\(P=12\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)

\(2P=\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{32}+1\right)\)

\(2P\)\(=\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)

\(2P=\)\(\left(5^8-1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)

\(2P=\left(5^{16}-1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)

\(2P=5^{32}-1\)

\(P=\dfrac{5^{32}-1}{2}\)