Question

cho a² -b² =4c² chứng minh rằng (5a-3b+8c)×(5a-3b-8c)=(3a-5b)²

Answer 1

Với: `x = 5a - 3b,y = 8c,` ta có:
`(5a - 3b + 8c)(5a - 3b - 8c) = (5a - 3b)^2 - (8c)^2  = (5a - 3b)^2 - 64c^2`
Từ `a^2 -  b^2 = 4c^2,` ta có:
`a^2 - b^2 = 4c^2`
`16 . (a^2 - b^2) = 16 . 4c^2`
`16a^2 - 16b^2 = 64c^2`
Thay `64c^2 = 16a^2 - 16b^2` vào, ta có:
`(5a -3b)^2 - 64c^2 = (5a - 3b)^2 - (16a^2- 16b^2)`
`=>  (5a - 3b)^2 - 64c^2 = 25a^2 - 30ab + 9b^2 - (16a^2 - 16b^2)`
`=> (5a - 3b)^2 - 64c^2 = 25a^2 - 30ab + 9b^2 - 16a^2 + 16b^2`
`=> (5a - 3b)^2 -64c^2 = 9a^2 - 30ab + 25b^2 = (3a - 5b)^2 (đpcm)`
Vậy: `(5a - 3b + 8c)(5a - 3b - 8c) = (3a - 5b)^2`