>368
x^4 +1 = (x^2 +1)^2 -2(x^2) = (x^2 +√2･x +1)(x^2 -√2･x +1)
　= {(x+1/√2)^2 +1/2}{(x-1/√2)^2 +1/2} = (u^2 +1/2)(v^2 +1/2).
　1/(x^4 +1) = (1/√8){ (x+√2)/(x^2+√2･x+1) - (x-√2)/(x^2-√2･x+1) }
　= (1/√8){ (u+1/√2)/(u^2 +1/2) - (v+1/√2)/(v^2+1/2) }.