Ta có :
`(a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2ac + 2bc`
`⇔ ab + ac + bc = 0`
`⇔ [ab + ac + bc]/[abc] = 0`
`⇔ [ab]/[abc] + [ac]/[abc] + [bc]/[abc] = 0`
`⇔ 1/a + 1/b + 1/c = 0`
`⇔ 1/a + 1/b = -1/c`
`⇔ [a+b]/[ab] = -1/c`
`⇔ (1/a + 1/b)² = (-1/c)³`
`⇔ 1/[a³] + 1/[b³] + 3 . 1/(a²) . 1/[b] + 3. 1/[b²] . 1/a = -1/(c³)`
`⇔ 1/[a³] + 1/[b³] + 1/[c³] + (3b+3a)/(a²b²) = 0`
`⇔ 1/[a³] + 1/[b³] + 1/[c³] + 3 . (-1/c) . 1/[ab] = 0`
`⇔ 1/a^2+1/b^2+1/c^2 - 3/[abc] = 0`
`⇔ 1/a^2+1/b^2+1/c^2=3/[abc]`
`⇔ ĐPCM`
Học tốt !
