Trình bày lời giải:
Nếu đề là:`(x-5)(2x-4)=5`
`(x-5) . (2x-4) = 5`
`=>x.(2x-4)-5.(2x-4)=5`
`=>2x^2-4x-10x+20=5`
`=>2x^2-4x-10x+20-5=0`
`=>2x^2+(-4x-10x)+15=0`
`=>2x^2-14x+15=0`
`=>2.(x^2-7.x+15/2)=0`
`=>x^2-7x+15/2=0`
`=>x^2-2.x. 7/2+(7/2)^2-19/4=0`
`=>x^2-x . 7/2-x. 7/2+7/2 . 7/2=0+19/4`
`=>x.(x-7/2)-7/2 . (x-7/2)=19/4`
`=>(x-7/2)(x-7/2)=19/4`
`=>(x-7/2)^2=19/4`
`=>(x-7/2)^2=(+-sqrt{19}/2)^2`
`=>[(x-7/2=sqrt{19}/2),(x-7/2=-sqrt{19}/2):}`
`=>[(x=(sqrt{19}+7)/2),(x=(-sqrt{19}+7)/2):}`
`=>[(x=(7+sqrt{19})/2),(x=(7-sqrt{19})/2):}`
Vậy `x=(7+sqrt{19})/2` hoặc `x=(7-sqrt{19})/2`
Nếu đề là:`(x-5)(2x-4)=0`
`=>[(x-5=0),(2x-4=0):}`
`=>[(x=0+5),(2x=0+4):}`
`=>[(x=5),(2x=4):}`
`=>[(x=5),(x=4:2):}`
`=>[(x=5),(x=2):}`
Vậy `x=5` hoặc `x=2`
