Toán cho A=9^45-27^29+3^86 chứng tỏ A chia hết cho 79 23/10/2021 By Everleigh cho A=9^45-27^29+3^86 chứng tỏ A chia hết cho 79
$\begin{array}{l} 9^{45}-27^{29}+3^{86} \\=(3^2)^{45}-(3^3)^{29} +3^{86}\\=3^{2.45}-3^{3.29}+3^{86}\\=3^{90}-3^{87}+3^{86}\\=3^{86}.3^4-3^{86}.3+3^{86}\\=3^{86}.(3^4-3+1)\\=3^{86}.(81-3+1)\\=3^{86}.79\,\,\vdots\,\,79\\\to 9^{45}-27^{29}+3^{86} \,\,\vdots\,\,79\\\to A \,\,\vdots\,\,79\,\,\rm(đpcm) \end{array}$ Trả lời
#KhanhHuyen2006 – Xin câu trả lời hay nhất `A = 9^{45} – 27^{29} + 3^{86}` `-> A = (3^2)^{45} – (3^3)^{29} + 3^{86}` `-> A = 3^{90} – 3^{87} + 3^{86}` `-> A = 3^{86} . 3^4 – 3^{86} . 3 + 3^{86} . 1` `-> A = 3^{86} . (3^4 – 3 + 1)` `-> A = 3^{86} . 79` `-> A = 3^{86} . 79 \vdots 79` `-> A = 9^{45} – 27^{29} + 3^{86} \vdots 79` (vì `3^{86} . 79 \vdots 79`) Trả lời
$\begin{array}{l} 9^{45}-27^{29}+3^{86} \\=(3^2)^{45}-(3^3)^{29} +3^{86}\\=3^{2.45}-3^{3.29}+3^{86}\\=3^{90}-3^{87}+3^{86}\\=3^{86}.3^4-3^{86}.3+3^{86}\\=3^{86}.(3^4-3+1)\\=3^{86}.(81-3+1)\\=3^{86}.79\,\,\vdots\,\,79\\\to 9^{45}-27^{29}+3^{86} \,\,\vdots\,\,79\\\to A \,\,\vdots\,\,79\,\,\rm(đpcm) \end{array}$
#KhanhHuyen2006 – Xin câu trả lời hay nhất
`A = 9^{45} – 27^{29} + 3^{86}`
`-> A = (3^2)^{45} – (3^3)^{29} + 3^{86}`
`-> A = 3^{90} – 3^{87} + 3^{86}`
`-> A = 3^{86} . 3^4 – 3^{86} . 3 + 3^{86} . 1`
`-> A = 3^{86} . (3^4 – 3 + 1)`
`-> A = 3^{86} . 79`
`-> A = 3^{86} . 79 \vdots 79`
`-> A = 9^{45} – 27^{29} + 3^{86} \vdots 79` (vì `3^{86} . 79 \vdots 79`)