`a + b + c = 0`
`<=> (a + b + c)^2 = 0`
`<=> a^2 + 2ab + 2ac + b^2 + 2bc + c^2 = 0`
`<=> (a^2 + b^2 + c^2) + 2(ab + ac + bc) = 0`
`<=> 14 + 2(ab + ac + bc) = 0`
`<=> 2(ab + ac + bc) = -14`
`<=> ab + ac + bc = -7`
`<=> (ab + ac + bc)^2 = (-7)^2`
`<=> (ab)^2 + 2a^2bc + 2ab^2c + (ac)^2 + 2abc^2 + (bc)^2 = 49`
`<=> (ab)^2 + (ac)^2 + (bc)^2 + 2abc(a + b + c) = 49`
`<=> (ab)^2 + (ac)^2 + (bc)^2 + 0 = 49`
`<=> (ab)^2 + (ac)^2 + (bc)^2 = 49`
Ta có: `a^2 + b^2 + c^2 = 14`
`<=> (a^2 + b^2 + c^2)^2 = 14^2`
`<=> a^4 + 2(ab)^2 + 2(ac)^2 + b^4 + 2(bc)^2 + c^4 = 196`
`<=> a^4 + b^4 + c^4 + 2[(ab)^2 + (ac)^2 + (bc)^2] = 196`
`<=> a^4 + b^4 + c^4 + 2. 49 = 196`
`<=> a^4 + b^4 + c^4 + 98 = 196`
`<=> a^4 + b^4 + c^4 = 98`
Vậy `a^4 + b^4 + c^4 = 98`
