Đặt `a/2=b/3=c/4=k⇒a=2k,b=3k,c=4k`
Thay `a=2k,b=3k,c=4k`
`⇒(2k)^2-(3k)^2+2.(4k)^2=108`
`⇒4k^2-9k^2+32k^2=108`
`⇒k^2(4-9+32)=108`
`⇒27k^2=108`
`⇒k^2=4`
`⇒k∈{2;-2}`
Thay `k=2`
`⇒a=2.2=4`
`⇒b=3.2=6`
`⇒c=4.2=8`
Thay `k=-2`
`⇒a=2.-2=-4`
`⇒b=3.-2=-6`
`⇒c=4.-2=-8`
Vậy `a=2,b=4,c=8` hoặc `a=-4,b=-6,c=-8`