Cho: ` a + b + c = 0 `
` a^2 + b^2 + c^2 = 2010 `
Tính: ` B = a^4 + b^4 + c^4 `
Cho: ` a + b + c = 0 ` ` a^2 + b^2 + c^2 = 2010 ` Tính: ` B = a^4 + b^4 + c^4 `
By Valentina
By Valentina
Cho: ` a + b + c = 0 `
` a^2 + b^2 + c^2 = 2010 `
Tính: ` B = a^4 + b^4 + c^4 `
Ta có :`a+b+c=0`
`⇒a^2+b^2+c^2+2(ab+bc+ca)=0`
`⇒2010+2(ab+bc+ca)=0`
`⇒ab+bc+ca=-1005`
`⇒a^2b^2+b^2c^2+c^2a^2+2abc(a+b+c)=1005^2`
`⇒a^2b^2+b^2c^2+c^2a^2=1005^2`
Lại có: `a^2+b^2+c^2=2010`
`⇒a^4+b^4+c^4+2(a^2b^2+b^2c^2+c^2a^2)=2010^2`
`⇒B=a^4+b^4+c^4=2010^2-2.1005^2=3.1005^2`
`Có a+b+c=0`
`⇒(a+b+c)²=0`
`⇒a²+b²+c²+2.(ab+bc+ac)=0`
`⇒ab+bc+ca=-2010`
`⇒(ab+bc+ca)²=4040100`
`⇒a²b²+b²c²+a²c²+2abc.(a+b+c)=4040100`
`⇒a²b²+b²c²+c²a²=4040100`
`Có a²+b²+c²=2010`
`⇒(a²+b²+c²)=4040100`
`⇒a^4+b^4+c^4+2.(a²b²+b²c²+c²a²)=4040100`
`⇒a^4+b^4+c^4=-4040100`
`Xin câu trả lời hay nhất`