已知a-1/a=3,求a^4+1/a^4的值

已知a-1/a=3,求a^4+1/a^4的值
已知a-1/a=3,求a^4+1/a^4的值

已知a-1/a=3,求a^4+1/a^4的值
a-1/a=3
所以 (a-1/a)²=a²+1/a²-2=9
a²+1/a²=11；
(a²+1/a²)²=a^4+1/a^4+2=121
故 a^4+1/a^4=119.

a^4+1/a^4
=(a^2+1/a^2)^2-2
=[(a-1/a)^2+2]^2-2
=[3^2+2]^2-2
=11^2-2
=121-2
=119

a^4+1/a^4
=a^4+1/a^4-2+2
=(a²-1/a²)²+2
=(a+1/a)²(a-1/a)²+2
=9(a+1/a)²+2
=9a²+18+9/a²+2
=9a²-18+9/a²+38
=9(a-1/a)²+38
=9×9+38
=119

对a-1/a=3进行两次平方，每一次平方后都要常数移到等式的右边

因为a-1/a=3 ；两边同时平方可得：a²+1/a²=11
（a²+1/a²）×（a²+1/a²）=a^4+1/a^4+2=121
所以a^4+1/a^4=119