`a+b+c = 0`
`⇔ (a+b+c)^2=0`
`⇔ a^2+b^2+c^2+2ab+2ac+2bc=0`
`⇔ 14+2(ab+bc+ac)=0`
`⇔ ab+bc+ca =-7`
`⇒ (ab+bc+ca)^2=49`
`⇔ a^2b^2+a^2c^2+b^2c^2+2a^2bc+2ab^2c+2abc^2=49`
`⇔ a^2b^2+a^2c^2+b^2c^2+2abc.0=49`
`⇔ a^2b^2+a^2c^2+b^2c^2 = 49`
Xét `a^2 + b^2 + c^2 = 14`
`⇒ (a^2+b^2+c^2)^2=196`
`⇔ a^4+b^4+c^4+2a^2b^2+2a^2c^2+2b^2c^2=196`
`⇔ a^4+b^4+c^4+2(a^2b^2+a^2c^2+b^2c^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 = 196 - 98 = 98`
Vậy `a^4 + b^4 + c^4 = 98`
Xin hay nhất ~
