若x加x分之1等于5,求x的2次方加x的2次方分之一和x的3次方加x的3次方分之一

用初一的方法做
2024-12-26 22:15:26
推荐回答(4个)
回答1:

(x+1/x)^=x^2+2x*(1/x)+(1/x)^2=x^2+(1/x)^+2
所以x^2+(1/x)^=(x+(1/x))^2-2=5*5-2=23
同理:(x+1/x)^3=x^3+3x^2(1/x)+3x(1/x)^2+(1/x)^3=x^3+(1/x)^3+3(x+1/x)=x^3+(1/x)^3+23*3
所以x^3+(1/x)^3=(x+(1/x))^3-23*3=125-69=56

回答2:

x+1/x=5 那么:
(x+1/x)^2=5^2=25=x^2+(1/x)^2+2
所以:
x^2+(1/x)^2=25-2=23
x^3+(1/x)^3=(x+1/x)*[x^2+(1/x)^2+1]=5*24=120

回答3:

x + 1/x = 5

(x + 1/x)^2
= x^2 + 1/x^2 + 2

x^2 + 1/x^2 = 25 - 2 = 23

(x + 1/x)^3
= x^3 + 3*x^2*(1/x) + 3*x*(1/x)^2 + 1/x^3
= (x^3 + 1/x^3) + 3(x + 1/x)
= (x^3 + 1/x^3) + 15

x^3 + 1/x^3 = 125 - 15 = 110

回答4:

x+1/x=5 (x+1/x)^2=25 x^2+1/x^2+2=25
x^2+1/x^2=23
(x+1/x)(x^2+1/x^2)=X^3+1/x+x+1/x^3=115
x^3+1/x^3+(x+1/x)=115
x+1/x=5
x^3+1/x^3=110

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