設(shè)aX^3=bY^3=cZ^3=k
則a=k/(x^3)
b=k/(y^3)
c=k/(z^3)
所以
左邊（3次根號(hào)ax^2+by^2+cz^2）
=3次根號(hào)(（k/(x^3)*x^2)+（k/(y^3)*y^2)+（k/(z^3)*z^2))
=3次根號(hào)(k/x+k/y+k/z)
=3次根號(hào)(k)
右邊(3次根號(hào)a+3次根號(hào)b+3次根號(hào)c)
=3次根號(hào)(k/(x^3))+3次根號(hào)(k/(y^3))+3次根號(hào)(k/(z^3))
=(1/x+1/y+1/z)*3次根號(hào)(k)
=3次根號(hào)(k)
所以左邊＝右邊