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~
\(3^{n+2}-2^{n+2}+3^n-2^n\)
\(=3^n.3^2-2^n.2^2+3^n-2^n\)
\(=3^n\left(3^2+1\right)-2^n\left(2^2+1\right)\)
\(=3^n.10-2^n.5\)
\(=3^n.10-2^{n-1}.10\)
\(=10.\left(3^n-2^{n-1}\right)⋮10\)
đpcm
Ball tự trình bày lại nhé~
a) \(A=\frac{2^{12}\cdot3^5-4^6\cdot9^2}{\left(2^3\cdot3\right)^6+8^4\cdot3^5}-\frac{5^{10}\cdot7^3-25^5\cdot49^2}{\left(125\cdot7\right)^3+5^9\cdot14^3}\)
\(A=\frac{2^{12}\cdot3^5-\left(2^2\right)^6\cdot\left(3^2\right)^2}{\left(2^3\right)^6\cdot3^6+\left(2^3\right)^4\cdot3^5}-\frac{5^{10}\cdot7^3-\left(5^2\right)^5\cdot\left(7^2\right)^2}{\left(5^3\right)^3\cdot7^3+5^9\cdot\left(2\cdot7\right)^3}\)
\(A=\frac{2^{12}\cdot3^5-2^{12}\cdot3^4}{2^{18}\cdot3^6+2^{12}\cdot3^5}-\frac{5^{10}\cdot7^3-5^{10}\cdot7^4}{5^9\cdot7^3+5^9\cdot2^3\cdot7^3}\)
\(A=\frac{2^{12}\cdot3^4\cdot\left(3-1\right)}{2^{12}\cdot3^5\cdot\left(2^6\cdot3+1\right)}-\frac{5^{10}\cdot7^3\cdot\left(1-7\right)}{5^9\cdot7^3\cdot\left(1+2^3\right)}\)
\(A=\frac{2}{579}-\frac{-10}{3}\)
\(A=\frac{2}{579}+\frac{10\cdot193}{579}\)
\(A=\frac{2+1930}{579}\)
\(A=\frac{644}{193}\)
Kkk, cảm ơn kudo, Thanh Phương nhiều nhé :)
