已知a+a（-1）=3,求下列各式的值(1)a(1/2)+a(-1/2)(2)a(2)-a(-2)(3)a3-a(-3)括号内为指数,

Question

已知a+a（-1）=3,求下列各式的值
(1)a(1/2)+a(-1/2)
(2)a(2)-a(-2)
(3)a3-a(-3)
括号内为指数,

Answer 1

(1)a(1/2)+a(-1/2)
a+1/a=(a½+a(-½))²-2=3;
∴a(1/2)+a(-1/2)=±√5;
(2)
(a-1/a)²=(a+1/a)²-4=9-4=5;
∴a-1/a=±√5;
a(2)-a(-2)
=(a+1/a)(a-1/a)
=±3√5;
(3)a3-a(-3)
=(a-1/a)(a²+1/a²+1)
=±√5×[(a+1/a)²-2+1]
=±√5×(9-2+1)
=±8√5;
括号内为指数,
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