If x, y and z are in continued proportion, then ` (x + y + z)(x-y+z)` = ______ .

Options

A. ` x^(2)-y^(2)+z^(2)`
B. ` x^(2)-y^(2)-z^(2)`
C. `x^(2)+y^(2)+z^(2)`
D. None of these

Answer

C

Explanation

(i) If x, y, z are in continued proportion, then `y^(2) = xz`.
(ii) First of all multiply the given expressions and simplify.
(iii) Substitute ` xz=y^(2)`, since x, y and z are in continued proportion.