`From a + b + c = 1`
`=> (a + b + c)^2 = 1^2`
`<=> a^2 + b^2 + c^2 + 2(ab + bc + ac) = 1 (+)`
`From 1/a + 1/b + 1/c = 0 (a, b, c ne 0)`
`=> (bc)/(abc) + (ac)/(abc) + (ab)/(abc) = 0`
`<=> (ac + bc + ab)/(abc) = 0 but abc ne 0`
`=> ac + bc + ab = 0`
`Replace ac + bc + ab t o (+), we have:`
`a^2 + b^2 + c^2 + 2. 0 = 1`
`<=> a^2 + b^2 + c^2 = 1`
`Wha t have t o proven`
