Question

已知x+1/x=a,求x²+1/x²和x的四次方+1/x的四次方的值.

Answer 1

∵x+1/x=a ∴（ X²+1）/x=a

x²+1/x²=[(x²+1）²-2x²]/x²=(x²+1）²/x²-2x²/x²=[（ X²+1）/x]²=a²-2

x的四次方+1/x的四次方=[（x的四次方+1）²-2x的四次方]/x的四次方=[(x²+1）²/x²-2x²/x²]²-2

={[（ X²+1）/x]²-2}²-2=（a²-2）²-2=a四次方-4a²+4-2=a四次方-4a²+2