&*** (20 9:44:5)1/χ+χ=3,则χ4+χ²+1/χ²=?

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&***(209:44:5)1/χ+χ=3,则χ4+χ²+1/χ²=?&***(209:44:5)1/χ+χ=3,则χ4+χ²+1/χ²=?&***(209:4

&*** (20 9:44:5)1/χ+χ=3,则χ4+χ²+1/χ²=?
&*** (20 9:44:5)
1/χ+χ=3,则χ4+χ²+1/χ²=?

&*** (20 9:44:5)1/χ+χ=3,则χ4+χ²+1/χ²=?
(x^4+x^2+1)/x^2
=x^2 +1/x^2 +1
=x^2 +1/x^2+2 -1
=(x+ 1/x)^2-1
=3^2-1
=8

∵x+1/x=3
∴x^2+1/x^2=9-2=7
∴(x^4+x^2+1)/x^2
=x^2+1+1/x^2
=7+1=8

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