已知a²+3a+1=0,求:⑴a+1/a;⑵a²+1/a²;⑶a³+1/a³;⑷a^4+1/a^4
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已知a²+3a+1=0,求:⑴a+1/a;⑵a²+1/a²;⑶a³+1/a³;⑷a^4+1/a^4
已知a²+3a+1=0,求:⑴a+1/a;⑵a²+1/a²;⑶a³+1/a³;⑷a^4+1/a^4
已知a²+3a+1=0,求:⑴a+1/a;⑵a²+1/a²;⑶a³+1/a³;⑷a^4+1/a^4
-3
7.
7
47
a²+3a+1=0
a² + 1 = -3a
a + 1/a = -3
a² + 1/a² = (-3)² - 2 = 7
a³ + 1/a³ = (a + 1/a)(a² + 1 + 1/a²) = (-3)*(7+1) = -24
a⁴+ 1/a⁴ = (a² + 1/a²)² - 2 = 49 - 2 = 47
a²+3a+1=0
(a²+3a+1)/a=0/a
a+1/a=-3 (1)
(a+1/a)²=(-3)²
a²+1/a²=7 (2)
(a²+1/a²)²=7²
a^4+1/a^4=47 (4)
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a²+3a+1=0
(a²+3a+1)/a=0/a
a+1/a=-3 (1)
(a+1/a)²=(-3)²
a²+1/a²=7 (2)
(a²+1/a²)²=7²
a^4+1/a^4=47 (4)
(a+1/a)³=(-3)³
a³+2a²(1/a)+a(1/a)²+a²(1/a)+2a(1/a)²+(1/a)³=-27
a³+1/a³+2a+1/a+a+2/a=-27
a³+1/a³+3(a+1/a)=-27
a³+1/a³+3(-3)=-27
a³+1/a³=-18 (3)
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