设a,b,c满足a+b+c=1,a^2+b^2+c^2=2,a^3+b^3+c^3=3.试求:(1)abc的值;(2)a^4+b^4+c^4的值.
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![设a,b,c满足a+b+c=1,a^2+b^2+c^2=2,a^3+b^3+c^3=3.试求:(1)abc的值;(2)a^4+b^4+c^4的值.](/uploads/image/z/12558875-59-5.jpg?t=%E8%AE%BEa%2Cb%2Cc%E6%BB%A1%E8%B6%B3a%2Bb%2Bc%3D1%2Ca%5E2%2Bb%5E2%2Bc%5E2%3D2%2Ca%5E3%2Bb%5E3%2Bc%5E3%3D3.%E8%AF%95%E6%B1%82%3A%281%29abc%E7%9A%84%E5%80%BC%3B%282%29a%5E4%2Bb%5E4%2Bc%5E4%E7%9A%84%E5%80%BC.)
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设a,b,c满足a+b+c=1,a^2+b^2+c^2=2,a^3+b^3+c^3=3.试求:(1)abc的值;(2)a^4+b^4+c^4的值.
设a,b,c满足a+b+c=1,a^2+b^2+c^2=2,a^3+b^3+c^3=3.试求:(1)abc的值;(2)a^4+b^4+c^4的值.
设a,b,c满足a+b+c=1,a^2+b^2+c^2=2,a^3+b^3+c^3=3.试求:(1)abc的值;(2)a^4+b^4+c^4的值.
因为(a+b+c)^2-2(ab+bc+ac)=a^2+b^2+c`2=2 所以ab+bc+ac=-1/2 ...A 因为a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-A) 所以abc=1/6 ...B 又a*2b^2+a*2c^2+b*2c^2=A^2-2(abca+abcb+abcc)=A^2-2abc(a+b+c)=-1/12 ...C 所以a^4+b^4+c^4=(a^2+b^2+c^2)^2-2C=25/6