Question

2道代数题!1.已知：x+1/x=3,求x^2/(x^4+x^2+1)的值.2.化简：√（7+4√3）+√(7-4√3)

Answer 1

1.

x+1/x=3,则x^2+1/x^2=(x+1/x)^2-2=7

x^2/(x^4+x^2+1)上下同除以x^2,

得1/(x^2+1/x^2+1)=1/(7+1)=1/8

2.

7+4√3=(2+√3)^2,

7-4√3=(2-√3)^2,

所以原式=2+√3+2-√3=4