21.当n为自然数时,有x^6n+1/x^6n=2 证明:(1)x+1/x=-1 ==>x^6n+1/x^6n=2 (2)x+1/x=1 ==>x^6n+1/x^6n=2 22.证明:(1)a^2+b^2+c^2+d^2-ab-bc-cd-da=0 ==>a=b=c=d (2)a^4+b^4+c^4+d^4-4abcd=0 ==>a=b=c=d
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![21.当n为自然数时,有x^6n+1/x^6n=2 证明:(1)x+1/x=-1 ==>x^6n+1/x^6n=2 (2)x+1/x=1 ==>x^6n+1/x^6n=2 22.证明:(1)a^2+b^2+c^2+d^2-ab-bc-cd-da=0 ==>a=b=c=d (2)a^4+b^4+c^4+d^4-4abcd=0 ==>a=b=c=d](/uploads/image/z/6183229-13-9.jpg?t=21.%E5%BD%93n%E4%B8%BA%E8%87%AA%E7%84%B6%E6%95%B0%E6%97%B6%2C%E6%9C%89x%5E6n%2B1%2Fx%5E6n%3D2+%E8%AF%81%E6%98%8E%EF%BC%9A%281%29x%2B1%2Fx%3D-1+%3D%3D%3Ex%5E6n%2B1%2Fx%5E6n%3D2+%282%29x%2B1%2Fx%3D1+%3D%3D%3Ex%5E6n%2B1%2Fx%5E6n%3D2+22.%E8%AF%81%E6%98%8E%EF%BC%9A%281%29a%5E2%2Bb%5E2%2Bc%5E2%2Bd%5E2-ab-bc-cd-da%3D0+%3D%3D%3Ea%3Db%3Dc%3Dd+%282%29a%5E4%2Bb%5E4%2Bc%5E4%2Bd%5E4-4abcd%3D0+%3D%3D%3Ea%3Db%3Dc%3Dd)
21.当n为自然数时,有x^6n+1/x^6n=2 证明:(1)x+1/x=-1 ==>x^6n+1/x^6n=2 (2)x+1/x=1 ==>x^6n+1/x^6n=2 22.证明:(1)a^2+b^2+c^2+d^2-ab-bc-cd-da=0 ==>a=b=c=d (2)a^4+b^4+c^4+d^4-4abcd=0 ==>a=b=c=d
21.当n为自然数时,有x^6n+1/x^6n=2
证明:(1)x+1/x=-1 ==>x^6n+1/x^6n=2
(2)x+1/x=1 ==>x^6n+1/x^6n=2
22.证明:(1)a^2+b^2+c^2+d^2-ab-bc-cd-da=0 ==>a=b=c=d
(2)a^4+b^4+c^4+d^4-4abcd=0 ==>a=b=c=d
21.当n为自然数时,有x^6n+1/x^6n=2 证明:(1)x+1/x=-1 ==>x^6n+1/x^6n=2 (2)x+1/x=1 ==>x^6n+1/x^6n=2 22.证明:(1)a^2+b^2+c^2+d^2-ab-bc-cd-da=0 ==>a=b=c=d (2)a^4+b^4+c^4+d^4-4abcd=0 ==>a=b=c=d
x^6n+1+1/x^6n=2
其实就是求证明 有x^6n+1/x^6n-2=0
两边同乘x^6n 就会得到 x^12n+2*x^6n-1=0
看着熟悉吧,其实就是(x^6n-1)^2=0
就是证明 有x^6n=1 下面不用说了吧,其实证明的我早忘记步骤了~看你自己的了~
第二个嘛,两边同乘以2 就的出 2*a^2+2*b^2+2*c^2+2*d^2-2*ab-2*bc-2*cd-2*da=0 熟悉吧,4个凑平方 (a-b)^2+(c-d)^2+(c-b)^2+(d-a)^2=0 着些数都大于0所以都等于0成立这样你再不会我就没办法了.
下一个接着凑平方 (a^2-b^2)^2+(c^2-d^2)^2+2*a^2*b^2+2*c^2*d^2-
4abcd=0 其实就是凑成平方然后把他们减去的都加上~
后面那部分很熟悉还是平方(a^2-b^2)^2+(c^2-d^2)^2+2(ab-cd)^2=0
别的不多说了,你按步骤写吧~