已知a+1/a=根号10,求a2+1/a2及a2-1/a2的值

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已知a+1/a=根号10,求a2+1/a2及a2-1/a2的值已知a+1/a=根号10,求a2+1/a2及a2-1/a2的值已知a+1/a=根号10,求a2+1/a2及a2-1/a2的值a+1/a=√

已知a+1/a=根号10,求a2+1/a2及a2-1/a2的值
已知a+1/a=根号10,求a2+1/a2及a2-1/a2的值

已知a+1/a=根号10,求a2+1/a2及a2-1/a2的值
a+1/a=√10,
两边平方,(a+1/a)^2=10
a^2+2*a*1/a+1/a^2=0
a^2+1/a^2=10-2=8
接下来求a-1/a
(a-1/a)^2
=a^2-2*a*1/a+1/a^2
=a^2+1/a^2-2
=8-2=6
则a-1/a=正负√6
a^2-1/a^2
=(a+1/a)*(a-1/a)
=√10*正负√6
=正负√60
=正负2√15

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