Question

√x2/x1 + √x1/x2 =怎么推导 用韦达定理推

Answer 1

显然有:

x1x2＝1/2,x1+x2＝-7/2.

①x2/x1+x1/x2

＝(x1^2+x2^2)/(x1x2)

＝[(x1+x2)^2-2x1x2]/(x1x2)

＝(49/4-2×1/2)/(1/2)

＝45/2.

②|x1-x2|

＝√[(x1+x2)^2-4x1x2]

＝√(49/4-4×1/2)

＝√41/2.

③√(x2/x1)+√(x1/x2)

＝(x1+x2)/√(x1x2)

＝(-7/2)/√(1/2)

＝(-7√2)/2.