Đáp án + Giải thích các bước giải:
d, `(x - 85)/15 + (x - 74)/13 + (x - 67)/11 + (x - 64)/9 = 10`
` (x - 85)/15 + (x - 74)/13 + (x - 67)/11 + (x - 64)/9 - 10 = 0`
` ( (x - 85)/15 - 1) + ( (x - 74)/13 - 2) + ( (x - 67)/11 - 3) + ( (x - 64)/9 - 4) = 0`
` ( x - 85 - 15)/15 + (x - 74 - 26)/13 + (x - 67 - 33)/11 + (x - 64 - 36)/9 = 0`
` (x - 100)/15 + (x - 100)/13 + (x - 100)/11 + (x - 100)/9 = 0`
` (x - 100) . ( 1/15 + 1/13 + 1/11 + 1/9) = 0`
Mà `1/15 + 1/13 + 1/11 + 1/9 \ne 0`
`=> x - 100 = 0`
` x = 0 + 100`
` x = 100`
Vậy phương trình có `S = {100}`
e, `(x - 1)/13 - (2x - 13)/15 = (3x - 15)/27 - (4x - 27)/29`
`( (x - 1)/13 - 1) - ( (2x - 13)/15 - 1) = ( (3x - 15)/27 - 1) - ( (4x - 27)/29 - 1)`
`(x - 1 - 13)/13 - (2x - 13 - 15)/15 = (3x - 15 - 27)/27 - (4x - 27 - 29)/29`
` (x - 14)/13 - (2x - 28)/15 = (2x - 42)/27 - (4x - 56)/29`
`=> (x - 14)/13 - (2x - 28)/15 - (2x - 42)/27 + (4x - 56)/29 = 0`
`=> (x - 14) . ( 1/13 - 2/15 - 3/27 + 4/29) = 0`
Mà `1/13 - 2/15 - 3/27 + 4/29 \ne 0`
`=> x - 14 = 0`
` x = 0 + 14`
` x = 14`
Vậy phương trình có `S = {14}`
