Question

数学问题[S/(u-v)]+[S/(u+v)]=S/v怎么得出u=(1+根号2)v求具体步骤.

Answer 1

[S/(u-v)]+[S/(u+v)]=S/v

1/(u-v)+1/(u+v)=1/v

v﹙u＋v﹚＋v﹙u－v﹚=﹙u＋v﹚﹙u－v﹚

vu＋v²＋vu－v²＝u²－v²

u²－2uv＝v²

u²－2uv＋v²＝2v²

﹙u－v﹚²＝2v²

u－v=√2v

u=﹙1＋√2﹚v