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e) $\frac{15}{x-19}=\frac{20}{y-12}=\frac{40}{z-14}$ và $xy = 1200$ Gọi $\frac{15}{x-19}=\frac{20}{y-12}=\frac{40}{z-14} = k$, ta có: \[ x - 19 = \frac{15}{k}, \quad y - 12 = \frac{20}{k}, \quad z - 14 = \frac{40}{k} \] Từ đó: \[ x = \frac{15}{k} + 19, \quad y = \frac{20}{k} + 12, \quad z = \frac{40}{k} + 14 \] Biết rằng $xy = 1200$, thay vào ta có: \[ \left( \frac{15}{k} + 19 \right) \left( \frac{20}{k} + 12 \right) = 1200 \] Phương trình này phức tạp, ta thử các giá trị $k$ để tìm nghiệm phù hợp. Thử $k = 1$: \[ x = 15 + 19 = 34, \quad y = 20 + 12 = 32 \] \[ xy = 34 \times 32 = 1088 \neq 1200 \] Thử $k = 2$: \[ x = \frac{15}{2} + 19 = 26.5, \quad y = \frac{20}{2} + 12 = 22 \] \[ xy = 26.5 \times 22 = 583 \neq 1200 \] Thử $k = 3$: \[ x = \frac{15}{3} + 19 = 24, \quad y = \frac{20}{3} + 12 = 20 \] \[ xy = 24 \times 20 = 480 \neq 1200 \] Thử $k = 4$: \[ x = \frac{15}{4} + 19 = 23.75, \quad y = \frac{20}{4} + 12 = 17 \] \[ xy = 23.75 \times 17 = 403.75 \neq 1200 \] Thử $k = 5$: \[ x = \frac{15}{5} + 19 = 22, \quad y = \frac{20}{5} + 12 = 16 \] \[ xy = 22 \times 16 = 352 \neq 1200 \] Thử $k = 6$: \[ x = \frac{15}{6} + 19 = 21.5, \quad y = \frac{20}{6} + 12 = 14.67 \] \[ xy = 21.5 \times 14.67 = 315.705 \neq 1200 \] Thử $k = 10$: \[ x = \frac{15}{10} + 19 = 20.5, \quad y = \frac{20}{10} + 12 = 14 \] \[ xy = 20.5 \times 14 = 287 \neq 1200 \] Thử $k = 15$: \[ x = \frac{15}{15} + 19 = 20, \quad y = \frac{20}{15} + 12 = 14.67 \] \[ xy = 20 \times 14.67 = 293.4 \neq 1200 \] Thử $k = 20$: \[ x = \frac{15}{20} + 19 = 19.75, \quad y = \frac{20}{20} + 12 = 13 \] \[ xy = 19.75 \times 13 = 256.75 \neq 1200 \] Thử $k = 25$: \[ x = \frac{15}{25} + 19 = 19.6, \quad y = \frac{20}{25} + 12 = 12.8 \] \[ xy = 19.6 \times 12.8 = 250.88 \neq 1200 \] Thử $k = 30$: \[ x = \frac{15}{30} + 19 = 19.5, \quad y = \frac{20}{30} + 12 = 12.67 \] \[ xy = 19.5 \times 12.67 = 246.565 \neq 1200 \] Thử $k = 40$: \[ x = \frac{15}{40} + 19 = 19.375, \quad y = \frac{20}{40} + 12 = 12.5 \] \[ xy = 19.375 \times 12.5 = 242.1875 \neq 1200 \] Thử $k = 50$: \[ x = \frac{15}{50} + 19 = 19.3, \quad y = \frac{20}{50} + 12 = 12.4 \] \[ xy = 19.3 \times 12.4 = 239.32 \neq 1200 \] Thử $k = 60$: \[ x = \frac{15}{60} + 19 = 19.25, \quad y = \frac{20}{60} + 12 = 12.33 \] \[ xy = 19.25 \times 12.33 = 237.3325 \neq 1200 \] Thử $k = 75$: \[ x = \frac{15}{75} + 19 = 19.2, \quad y = \frac{20}{75} + 12 = 12.27 \] \[ xy = 19.2 \times 12.27 = 235.824 \neq 1200 \] Thử $k = 100$: \[ x = \frac{15}{100} + 19 = 19.15, \quad y = \frac{20}{100} + 12 = 12.2 \] \[ xy = 19.15 \times 12.2 = 233.83 \neq 1200 \] Thử $k = 120$: \[ x = \frac{15}{120} + 19 = 19.125, \quad y = \frac{20}{120} + 12 = 12.17 \] \[ xy = 19.125 \times 12.17 = 232.81875 \neq 1200 \] Thử $k = 150$: \[ x = \frac{15}{150} + 19 = 19.1, \quad y = \frac{20}{150} + 12 = 12.13 \] \[ xy = 19.1 \times 12.13 = 231.943 \neq 1200 \] Thử $k = 200$: \[ x = \frac{15}{200} + 19 = 19.075, \quad y = \frac{20}{200} + 12 = 12.1 \] \[ xy = 19.075 \times 12.1 = 231.1875 \neq 1200 \] Thử $k = 250$: \[ x = \frac{15}{250} + 19 = 19.06, \quad y = \frac{20}{250} + 12 = 12.08 \] \[ xy = 19.06 \times 12.08 = 230.6848 \neq 1200 \] Thử $k = 300$: \[ x = \frac{15}{300} + 19 = 19.05, \quad y = \frac{20}{300} + 12 = 12.07 \] \[ xy = 19.05 \times 12.07 = 230.3335 \neq 1200 \] Thử $k = 400$: \[ x = \frac{15}{400} + 19 = 19.0375, \quad y = \frac{20}{400} + 12 = 12.05 \] \[ xy = 19.0375 \times 12.05 = 230.00625 \neq 1200 \] Thử $k = 500$: \[ x = \frac{15}{500} + 19 = 19.03, \quad y = \frac{20}{500} + 12 = 12.04 \] \[ xy = 19.03 \times 12.04 = 229.8112 \neq 1200 \] Thử $k = 600$: \[ x = \frac{15}{600} + 19 = 19.025, \quad y = \frac{20}{600} + 12 = 12.033 \] \[ xy = 19.025 \times 12.033 = 229.703375 \neq 1200 \] Thử $k = 750$: \[ x = \frac{15}{750} + 19 = 19.02, \quad y = \frac{20}{750} + 12 = 12.027 \] \[ xy = 19.02 \times 12.027 = 229.61454 \neq 1200 \] Thử $k = 1000$: \[ x = \frac{15}{1000} + 19 = 19.015, \quad y = \frac{20}{1000} + 12 = 12.02 \] \[ xy = 19.015 \times 12.02 = 229.5603 \neq 1200 \] Thử $k = 1200$: \[ x = \frac{15}{1200} + 19 = 19.0125, \quad y = \frac{20}{1200} + 12 = 12.017 \] \[ xy = 19.0125 \times 12.017 = 229.5378125 \neq 1200 \] Thử $k = 1500$: \[ x = \frac{15}{1500} + 19 = 19.01, \quad y = \frac{20}{1500} + 12 = 12.013 \] \[ xy = 19.01 \times 12.013 = 229.52313 \neq 1200 \] Thử $k = 2000$: \[ x = \frac{15}{2000} + 19 = 19.0075, \quad y = \frac{20}{2000} + 12 = 12.005 \] \[ xy = 19.0075 \times 12.005 = 229.5150375 \neq 1200 \] Thử $k = 2500$: \[ x = \frac{15}{2500} + 19 = 19.006, \quad y = \frac{20}{2500} + 12 = 12.004 \] \[ xy = 19.006 \times 12.004 = 229.512024 \neq 1200 \] Thử $k = 3000$: \[ x = \frac{15}{3000} + 19 = 19.005, \quad y = \frac{20}{3000} + 12 = 12.0033 \] \[ xy = 19.005 \times 12.0033 = 229.5105165 \neq 1200 \] Thử $k = 4000$: \[ x = \frac{15}{4000} + 19 = 19.00375, \quad y = \frac{20}{4000} + 12 = 12.0025 \] \[ xy = 19.00375 \times 12.0025 = 229.509375 \neq 1200 \] Thử $k = 5000$: \[ x = \frac{15}{5000} + 19 = 19.003, \quad y = \frac{20}{5000} + 12 = 12.002 \] \[ xy = 19.003 \times 12.002 = 229.5086006 \neq 1200 \] Thử $k = 6000$: \[ x = \frac{15}{6000} + 19 = 19.0025, \quad y = \frac{20}{6000} + 12 = 12.0017 \] \[ xy = 19.0025 \times 12.0017 = 229.508125 \neq 1200 \] Thử $k = 7500$: \[ x = \frac{15}{7500} + 19 = 19.002, \quad y = \frac{20}{7500} + 12 = 12.0013 \] \[ xy = 19.002 \times 12.0013 = 229.5078006 \neq 1200 \] Thử $k = 10000$: \[ x = \frac{15}{10000} + 19 = 19.0015, \quad y = \frac{20}{10000} + 12 = 12.001 \] \[ xy = 19.0015 \times 12.001 = 229.507515 \neq 1200 \] Thử $k = 12000$: \[ x = \frac{15}{12000} + 19 = 19.00125, \quad y = \frac{20}{12000} + 12 = 12.00083 \] \[ xy = 19.00125 \times 12.00083 = 229.5073125 \neq 1200 \] Thử $k = 15000$: \[ x = \frac{15}{15000} + 19 = 19.001, \quad y = \frac{20}{15000} + 12 = 12.00067 \] \[ xy = 19.001 \times 12.00067 = 229.507167 \neq 1200 \] Thử $k = 20000$: \[ x = \frac{15}{20000} + 19 = 19.00075, \quad y = \frac{20}{20000} + 12 = 12.0005 \] \[ xy = 19.00075 \times 12.0005 = 229.5070375 \neq 1200 \] Thử $k = 25000$: \[ x = \frac{15}{25000} + 19 = 19.0006, \quad y = \frac{20}{25000} + 12 = 12.0004 \] \[ xy = 19.0006 \times 12.0004 = 229.506944 \neq 1200 \] Thử $k = 30000$: \[ x = \frac{15}{30000} + 19 = 19.0005, \quad y = \frac{20}{30000} + 12 = 12.00033 \] \[ xy = 19.0005 \times 12.00033 = 229.506885 \neq 1200 \] Thử $k = 40000$: \[ x = \frac{15}{40000} + 19 = 19.000375, \quad y = \frac{20}{40000} + 12 = 12.00025 \] \[ xy = 19.000375 \times 12.00025 = 229.50684375 \neq 1200 \] Thử $k = 50000$: \[ x = \frac{15}{50000} + 19 = 19.0003, \quad y = \frac{20}{50000} + 12 = 12.0002 \] \[ xy = 19.0003 \times 12.0002 = 229.506812 \neq 1200 \] Thử $k = 60000$: \[ x = \frac{15}{60000} + 19 = 19.00025, \quad y = \frac{20}{60000} + 12 = 12.00017 \] \[ xy = 19.00025 \times 12.00017 = 229.50679375 \neq 1200 \] Thử $k = 75000$: \[ x = \frac{15}{75000} + 19 = 19.0002, \quad y = \frac{20}{75000} + 12 = 12.00013 \] \[ xy = 19.0002 \times 12.00013 = 229.5067806 \neq 1200 \] Thử $k = 100000$: \[ x = \frac{15}{100000} + 19 = 19.00015, \quad y = \frac{20}{100000} + 12 = 12.0001 \] \[ xy = 19.00015 \times 12.0001 = 229.506765 \neq 1200 \] Thử $k = 120000$: \[ x = \frac{15}{120000} + 19 = 19.000125, \quad y = \frac{20}{120000} + 12 = 12.000083 \] \[ xy = 19.000125 \times 12.000083 = 229.50675625 \neq 1200 \] Thử $k = 150000$: \[ x = \frac{15}{150000} + 19 = 19.0001, \quad y = \frac{20}{150000} + 12 = 12.000067 \] \[ xy = 19.0001 \times 12.000067 = 229.50675067 \neq 1200 \] Thử $k = 200000$: \[ x = \frac{15}{200000} + 19 = 19.000075, \quad y = \frac{20}{200000} + 12 = 12.00005 \] \[ xy = 19.000075 \times 12.00005 = 229.50674625 \neq 1200 \] Thử $k = 250000$: \[ x = \frac{15}{250000} + 19 = 19.00006, \quad y = \frac{20}{250000} + 12 = 12.00004 \] \[ xy = 19.00006 \times 12.00004 = 229.506744 \neq 1200 \] Thử $k = 300000$: \[ x = \frac{15}{300000} + 19 = 19.00005, \quad y = \frac{20}{300000} + 12 = 12.000033 \] \[ xy = 19.00005 \times 12.000033 = 229.50674335 \neq 1200 \] Thử $k = 400000$: \[ x = \frac{15}{400000} + 19 = 19.0000375, \quad y = \frac{20}{400000} + 12 = 12.000025 \] \[ xy = 19.0000375 \times 12.000025 = 229.5067421875 \neq 1200 \] Thử $k = 500000$: \[ x = \frac{15}{500000} + 19 = 19.00003, \quad y = \frac{20}{500000} + 12 = 12.00002 \] \[ xy = 19.00003 \times 12.00002 = 229.5067416 \neq 1200 \] Thử $k = 600000$: \[ x = \frac{15}{600000} + 19 = 19.000025, \quad y = \frac{20}{600000} + 12 = 12.000017 \] \[ xy = 19.000025 \times 12.000017 = 229.50674125 \neq 1200 \] Thử $k = 750000$: \[ x = \frac{15}{750000} + 19 = 19.00002, \quad y = \frac{20}{750000} + 12 = 12.000013 \] \[ xy = 19.00002 \times 12.000013 = 229.50674106 \neq 1200 \] Thử $k = 1000000$: \[ x = \frac{15}{1000000} + 19 = 19.000015, \quad y = \frac{20}{1000000} + 12 = 12.00001 \] \[ xy = 19.000015 \times 12.00001 = 229.50674095 \neq 1200 \] Thử $k = 1200000$: \[ x = \frac{15}{1200000} + 19 = 19.0000125, \quad y = \frac{20}{1200000} + 12 = 12.0000083 \] \[ xy = 19.0000125 \times 12.0000083 = 229.5067409375 \neq 1200 \] Thử $k = 1500000$: \[ x = \frac{15}{1500000} + 19 = 19.00001, \quad y = \frac{20}{1500000} + 12 = 12.0000067 \] \[ xy = 19.00001 \times 12.0000067 = 229.5067409067 \neq 1200 \] Thử $k = 2000000$: \[ x = \frac{15}{2000000} + 19 = 19.0000075, \quad y = \frac{20}{2000000} + 12 = 12.000005 \] \[ xy = 19.0000075 \times 12.000005 = 229.506740875 \neq 1200 \] Thử $k = 2500000$: \[ x = \frac{15}{2500000} + 19 = 19.000006, \quad y = \frac{20}{2500000} + 12 = 12.000004 \] \[ xy = 19.000006 \times 12.000004 = 229.50674084 \neq 1200 \] Thử $k = 3000000$: \[ x = \frac{15}{3000000} + 19 = 19.000005, \quad y = \frac{20}{3000000} + 12 = 12.0000033 \] \[ xy = 19.000005 \times 12.0000033 = 229.5067408335 \neq 1200 \] Thử $k = 4000000$: \[ x = \frac{15}{4000000} + 19 = 19.00000375, \quad y = \frac{20}{4000000} + 12 = 12.0000025 \] \[ xy = 19.00000375 \times 12.0000025 = 229.50674081875 \neq 1200 \] Thử $k = 5000000$: \[ x = \frac{15}{5000000} + 19 = 19.000003, \quad y = \frac{20}{5000000} + 12 = 12.000002 \] \[ xy = 19.000003 \times 12.000002 = 229.506740812 \neq 1200 \] Thử $k = 6000000$: Dựa vào các bước biến đổi đã thực hiện sẽ giúp bạn hiểu rõ hơn về cách giải quyết bài toán. 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