设x
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设x设x设xx-1/x=根号5--->x^2-根号5*x-1=0解得x=(根号5-3)/2(因为x小於0)并令a=(根号5-3)/2f(x)=x^2-根号5*x-1b(x)=x^10+x^6+x^4+
设x
设x
设x
x - 1/x = 根号5 ---> x^2 - 根号5*x -1 =0 解得x = (根号5 - 3)/2 (因为x小於0) 并令a = (根号5 - 3)/2 f(x) = x^2 - 根号5*x -1 b(x) = x^10+x^6+x^4+1 c(x) = x^10+x^8+x^2+1 则f(a) = 0 利用长除法求得(可利用一点技巧) b(x) / f(x)之余式为42( 55根号5 * x + 47) --->设商为g(x) c(x) / f(x)之余式为47( 55根号5 * x + 47) --->设商为g'(x) 设原式 = F(x) = b(x)/c(x) = [ f(x) * g(x) + 42( 55根号5 * x + 47) ] / [ f(x) * g'(x) + 47( 55根号5 * x + 47) ] 则F(a) = [ f(a) * g(a) + 42( 55根号5 * a + 47) ] / [ f(a) * g'(a) + 47( 55根号5 * a + 47) ] = 42( 55根号5 * a + 47) / 47( 55根号5 * a + 47) = 42/47