√x2/x1 + √x1/x2 =怎么推导用韦达 - 知识问答

√x2/x1 + √x1/x2 =怎么推导用韦达定理推

1个回答

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.

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