已知正整数x,y,z,w满足2007x^2=2008y^2=2009z^2=2010w^2,且1/x + 1/y + 1/z+ 1/w =1.（问题见下）求根号下2007x+2008y+2009z+2010w的值.

已知正整数x,y,z,w满足2007x^2=2008y^2=2009z^2=2010w^2,且1/x + 1/y + 1/z+ 1/w =1.（问题见下）求根号下2007x+2008y+2009z+2010w的值.
已知正整数x,y,z,w满足2007x^2=2008y^2=2009z^2=2010w^2,且1/x + 1/y + 1/z+ 1/w =1.（问题见下）
求根号下2007x+2008y+2009z+2010w的值.

已知正整数x,y,z,w满足2007x^2=2008y^2=2009z^2=2010w^2,且1/x + 1/y + 1/z+ 1/w =1.（问题见下）求根号下2007x+2008y+2009z+2010w的值.
2007x^2=2008y^2=2009z^2=2010w^2 ＝ k
所以2007x = k/x,2008y= k/y,2009z = k/z,2010w =k/w,
所以√(2007x) + √(2008y)+√(2009z)+√(2010w) = √k (1/√x+1/√y+1/√z+1/√w)
=√k(1/√(k/2007) + 1/√(k/2008) + 1/√(k/2009) + 1/√(k/2010))
=1/√2007 + 1/√2008 + 1/√2009 + 1/√2010