已知a+1/a=3,求下列式子的值(1)a^2+1/a^2(2)a^3+1/a^3(3)a^4+1/a^4
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已知a+1/a=3,求下列式子的值(1)a^2+1/a^2(2)a^3+1/a^3(3)a^4+1/a^4
已知a+1/a=3,求下列式子的值
(1)a^2+1/a^2
(2)a^3+1/a^3
(3)a^4+1/a^4
已知a+1/a=3,求下列式子的值(1)a^2+1/a^2(2)a^3+1/a^3(3)a^4+1/a^4
(1)a^2+1/a^2
=(a+1/a)^2-2
=9-2
=7
(2)a^3+1/a^3
=(a+1/a)(a^2-1+1/a^2)
=3*(7-1)
=18
(3)a^4+1/a^4
=(a^2+1/a^2)^2-2
=49-2
=47
a+1/a=3
(a+1/a)^2=a^2+1/a^2+2=9
(1)a^2+1/a^2=9-2=7
(2)a^3+1/a^3=(a+1/a)(a^2+1/a^2-1)=3(7-1)=18
a^2+1/a^2=7
(a^2+1/a^2)^2=a^4+1/a^4+2=49
(3)a^4+1/a^4=49-2=47
(1)a^2+1/a^2= 7
(2)a^3+1/a^3=18
(3)a^4+1/a^4=47
(1)
把a+1/a=3两边同时平方:
a²+2+1/a²=9
∴a²+1/a²=7
(2)
(a²+1/a²)(a+1/a)=3*7
∴a^3+1/a^3+a+1/a=21
∴a^3+1/a^3=21-3=18
(3)把a²+1/a²=7两边同时平方:
a^4+1/a^4+2=49
a^4+1/a^4=47
a+1/a=3 a=0.5 你算出来就行了