Question

A proportion question ​

Answer 1

because x,y,z are in continuous proportion

=> x/y = y/z

<=> xz = y² =>

`(xz)/(y) =y\\\\=>(x^(3)z^(3) )/(y^(3) )=y^(3)`(1)

with (1), we have:

`x^(2)y^(2)z^(2)((1)/(x^(3) )+(1)/(y^(3) )+(1)/(z^(3) ))\\\\= (xyz)^(2)((1)/(x^(3) ) +(y^(3) )/(x^(3)z^(3) )+(1)/(z^(3) ))\\\\=(xyz)^(2) ((x^(3)+y^(3)+z^(3) )/(x^(3)z^(3)) )\\\\=y^(2).(x^(3)+y^(3)+z^(3) )/(xz) \\\\= xz.(x^(3)+y^(3)+z^(3) )/(xz) \\\\=x^(3)+y^(3)+z^(3)`

Explanation: