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Đặt d=ƯCLN(12n+1;30n+2)
=>12n+1 chia hết cho d; 30n+2 chia hết cho d
=>5(12n+1) chia hết cho d; 2(30n+2) chia hết cho d
=>60n+5 chia hết cho d; 60n+4 chia hết cho d
=>(60n+5)-(60n+4) chia hết cho d
=>1 chia hết cho d
=>d=1
=>phân số \(\frac{12n+1}{30n+2}\) là phân số tối giản
Bài 1:
\(\frac{2^{12}.3^5-4^6.9^2}{\left(2^2.3\right)^6+8^4.3^2}-\frac{5^{10}.7^3-25^3.49^2}{\left(125.7\right)^3+5^9.14^3}=\frac{2^{12}.3^5-\left(2^2\right)^6.\left(3^2\right)^2}{2^{12}.3^6+\left(2^3\right)^4.3^2}-\frac{5^{10}.7^3-\left(5^2\right)^3.\left(7^2\right)^2}{\left(5^3.7\right)^3+5^9.2^3.7^3}\)
\(=\frac{2^{12}.3^5-2^{12}.3^4}{2^{12}.3^6+2^{12}.3^2}-\frac{5^{10}.7^3-5^6.7^4}{5^9.7^3+5^9.2^3.7^3}=\frac{2^{12}.3^4\left(3-1\right)}{2^{12}.3^2\left(3^4+1\right)}-\frac{5^6.7^3\left(5^4-7\right)}{5^9.7^3\left(1+2^3\right)}=\frac{3^2.2}{82}-\frac{618}{5^3.9}\)
\(=\frac{9}{41}-\frac{206}{375}=\)
a hơi dài để làm phần b trước :
\(3^{n+2}-2^{n+2}+3^n-2^n\)
\(=3^n\cdot3^2-2^n\cdot2^2+3^n-2^n\)
\(=\left(3^n\cdot3^2+3^n\right)-\left(2^n\cdot2^2+2^n\right)\)
\(=3^n\cdot\left(3^2+1\right)-2^n\cdot\left(2^2+1\right)\)
\(=3^n\cdot10-2^n\cdot5\)
\(=3^n\cdot10-2^{n-1}\cdot2\cdot5\)
\(=3^n\cdot10-2^{n-1}\cdot10\)
\(=10\cdot\left(3^n-2^{n-1}\right)⋮10\left(đpcm\right)\)
\(A=\frac{2^{12}.3^5-4^6.9^2}{\left(2^3.3\right)^6+8^4.3^5}-\frac{5^{10}.7^3-25^5.49^2}{\left(125.7\right)^3+5^9.14^3}\)
\(A=\frac{2^{12}.3^5-\left(2^2\right)^6.\left(3^2\right)^2}{\left(2^3.3\right)^6+\left(2^3\right)^4.3^5}-\frac{5^{10}.7^3-\left(5^2\right)^5.\left(7^2\right)^2}{\left(5^3.7\right)^3+5^9.\left(2.7\right)^3}\)
\(A=\frac{2^{12}.3^5-2^{12}.3^4}{2^{18}.3^6+2^{12}.3^5}-\frac{5^{10}.7^3-5^{10}.7^4}{5^9.7^3+5^9.2^3.7^3}\)
\(A=\frac{2^{12}.3^4\left(3-1\right)}{2^{12}.3^5.\left(2^6-1\right)}-\frac{5^{10}.7^3.\left(1-7\right)}{5^9.7^3\left(1+2^3\right)}\)
\(A=\frac{2}{3.\left(64-1\right)}-\frac{5.\left(-6\right)}{9}\)
\(A=\frac{2}{3.63}+\frac{30}{9}\)
Tự lm tiếp Ball nhé~
a:Sửa đề: \(A=\dfrac{2^{12}\cdot3^5-2^{12}\cdot3^3}{2^{12}\cdot3^6+2^{12}\cdot3^5}-\dfrac{5^{10}\cdot7^3-25^5\cdot7^4}{5^9\cdot7^3+5^9\cdot2^3\cdot7^3}\)
\(=\dfrac{2^{12}\cdot3^3\cdot\left(3^2-1\right)}{2^{12}\cdot3^5\left(3+1\right)}-\dfrac{5^{10}\cdot7^3-5^{10}\cdot7^4}{5^9\cdot7^3\cdot9}\)
\(=\dfrac{1}{9}\cdot\dfrac{8}{4}-\dfrac{5^{10}\cdot7^3\cdot\left(1-7\right)}{5^9\cdot7^3\cdot9}\)
\(=\dfrac{2}{9}-\dfrac{5\cdot\left(-2\right)}{3}=\dfrac{2}{9}+\dfrac{10}{3}=\dfrac{2+30}{9}=\dfrac{32}{9}\)
b: Sửa đề: \(3^{n+2}-2^{n+2}+3^n-2^n\)
\(=3^n\cdot9+3^n-2^n\cdot4-2^n\)
\(=3^n\cdot10-2^n\cdot5\)
\(=10\left(3^n-2^{n-1}\right)⋮10\)
\(A=\dfrac{2^{12}\cdot3^5-2^{12}\cdot3^4}{2^{12}\cdot3^6+2^{12}\cdot3^5}-\dfrac{5^{10}\cdot7^3-5^{10}\cdot7^4}{5^9\cdot7^3+5^9\cdot7^3\cdot8}\)
\(=\dfrac{3^4\cdot\left(3-1\right)}{3^5\left(3+1\right)}-\dfrac{5^{10}\cdot7^3\cdot\left(-6\right)}{5^9\cdot7^3\cdot9}=\dfrac{2}{3\cdot4}-\dfrac{5\cdot\left(-2\right)}{3}\)
\(=\dfrac{1}{6}+\dfrac{10}{3}=\dfrac{1}{6}+\dfrac{20}{6}=\dfrac{21}{6}=\dfrac{7}{2}\)
\(=\frac{2^{12}.2^5-2^{12}.3^4}{2^{12}.3^6+2^{12}.3^5}-\frac{5^{10}.7^3-5^{10}.7^4}{5^9.7^3+5^9.2^3.7^3}\)
\(=\frac{2^{12}.3^4.\left(3-1\right)}{2^{12}.3^5.\left(3+1\right)}-\frac{5^{10}.7^3.\left(1-7\right)}{5^9.7^3.\left(1+2^3\right)}\)
\(=\frac{2^{12}.3^4.2}{2^{12}.3^5.4}-\frac{5^{10}.7^3.\left(-6\right)}{5^9.7^3.9}\)
\(=\frac{1}{6}-\frac{-10}{3}\)
\(\frac{1}{6}-\frac{-20}{6}=\frac{7}{2}\)
\(\frac{2^{12}.3^5-4^6.9^2}{\left(2^2.3\right)^6+8^4.3^5}-\frac{5^{10}.7^3-25^5.49^2}{\left(125.7\right)^3+5^9.14^3}=\frac{2^{12}.3^5-\left(2^2\right)^6.\left(3^2\right)^2}{2^{12}.3^6+\left(2^3\right)^4.3^5}-\frac{5^{10}.7^3-\left(5^2\right)^5.\left(7^2\right)^2}{\left(5^3.7\right)^3+5^9.2^3.7^3}\)
\(=\frac{2^{12}.3^5-2^{12}.3^4}{2^{12}.3^6+2^{12}.3^5}-\frac{5^{10}.7^3-5^{10}.7^4}{5^9.7^3+5^9.2^3.7^3}=\frac{2^{12}.3^4\left(3-1\right)}{2^{12}.3^5\left(3+1\right)}-\frac{5^{10}.7^3\left(1-7\right)}{5^9.7^3\left(1+2^3\right)}=\frac{2}{3.4}-\frac{5.\left(-6\right)}{9}\)
\(=\frac{1}{6}-\frac{-10}{3}=\frac{1}{6}-\frac{-20}{6}=\frac{21}{6}=\frac{7}{2}\)
Lẽ ra là làm xong cho bạn rồi, vậy mà tự nhiên máy sập, giờ chép lại, oải quá :|