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a,
\(5^{x+4}-3.5^{x+3}=2.5^{11}\)
\(\Rightarrow5^{x+3}\left(5-3\right)=2.5^{11}\)
\(\Rightarrow5^{x+3}2=2.5^{11}\)
\(\Rightarrow5^{x+3}=5^{11}\)
\(\Rightarrow x+3=11\)
\(\Rightarrow x=8\)
b, (Check lai xem de sai o dau khong nhe)
\(3.5^{x+2}+4.5^{x+3}=19.5^{10}\)
Dat 5x ra ben ngoai
\(\Rightarrow5^x.5^23+5^x:5^{-3}.4\)
\(\Rightarrow5^x\left(5^2.3+5^{-3}.4\right)\)
\(\Rightarrow5^x\left(5^{-3}.5^5.3+5^{-3}.4\right)\)
\(\Rightarrow5^x[5^{-3}\left(5^53+4\right)\)
\(\Rightarrow5^x[5^{-3}\left(3125.3+4\right)\)
\(\Rightarrow5^x\left(5^{-3}\right).9379\)
=> Khong tim duoc gia tri cua x \(\Rightarrow x\in\varnothing\)
\(\dfrac{9}{14}-\dfrac{5}{8}+\dfrac{3}{7}=\dfrac{36}{56}-\dfrac{35}{56}+\dfrac{24}{56}=\dfrac{25}{56}\)
\(\dfrac{2}{9}-\dfrac{7}{10}+\dfrac{4}{5}=\dfrac{20}{90}-\dfrac{63}{90}+\dfrac{72}{90}=\dfrac{29}{90}\)
\(\dfrac{8}{19}+\dfrac{7}{5}-\dfrac{9}{20}+\dfrac{11}{12}=\dfrac{8}{19}+\dfrac{84}{60}-\dfrac{27}{60}+\dfrac{55}{60}=\dfrac{8}{19}+\dfrac{112}{60}=\dfrac{8}{19}+\dfrac{28}{15}=\dfrac{652}{285}\)
\(-\dfrac{11}{12}+\dfrac{7}{8}+\dfrac{1}{10}\)
\(=-\dfrac{1}{24}+\dfrac{1}{10}\)
\(=\dfrac{7}{120}\)
chỉ với
\(-\dfrac{3}{7}.\dfrac{5}{7}+\left(-\dfrac{5}{7}\right).\dfrac{8}{11}+\dfrac{19}{7}\\ =\dfrac{5}{7}.\left(-\dfrac{3}{7}-\dfrac{8}{11}\right)+\dfrac{19}{7}\\ =\dfrac{5}{7}.-\dfrac{89}{77}+\dfrac{19}{7}\\ =\dfrac{445}{539}+\dfrac{19}{7}\\ =\dfrac{1908}{539}\)