阅读第一题的解答过程,再解答第二题.(1)已知x+x^-1=5,求x^3+x^-3的值.因为x+x^

发布时间:2021-02-19 09:46:49

阅读第一题的解答过程,再解答第二题.(1)已知x+x^-1=5,求x^3+x^-3的值.因为x+x^-2=(x+x^-1)^2-2=5^2-2=23所以x^3+x^-3=(x+x^-1)(x^2+x^-2)-(x乘以x^-2+x^-1乘以x^2)=(x+x^-1)(x^2+x^-2)-(x^-1+x)=5乘以23-5=110.(2)若x+x^-1=3,求x^5+x^-5的值.请注意:比如x+x^-

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(x)这个地方是(x^2)+x^-2=(x+x^-1)^2-2=5^2-2=23 x^2+x^-2=(x+x^-1)^2-2=3^2-2=7x^3+x^-3=(x+x^-1)(x^2+x^-2)-(x乘以x^-2+x^-1乘以x^2)=(x+x^-1)(x^2+x^-2)-(x^-1+x)=3乘以7-3=18x^5+x^-5=(x^2+x^-2)(x^3+x^-3)-(x^...
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