3,已知:a+1/a=3,⑴求a²+1/a²的值 ⑵求a⁴+1/a⁴的值.
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3,已知:a+1/a=3,⑴求a²+1/a²的值 ⑵求a⁴+1/a⁴的值.
3,已知:a+1/a=3,⑴求a²+1/a²的值 ⑵求a⁴+1/a⁴的值.
3,已知:a+1/a=3,⑴求a²+1/a²的值 ⑵求a⁴+1/a⁴的值.
解
a+1/a=3
两边平方
(a+1/a)²=9
即a²+2+1/a²=9
∴a²+1/a²=7
再次平方
(a²+1/a²)²=49
即a^4+2+1/a^4=49
∴a^4+1/a^4=47