If x, y and z are in continued proportion then $z : x :: z^{2} :$ ____.

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Solution

If x, y, and z are in continued proportion then $y^{2} = x z$
Multiply both sides of the equation by z
Equation becomes, $z y^{2} = x z^{2}$
$⟹ \frac{z}{x} = \frac{z^{2}}{y^{2}}$
$⟹ z : x :: z^{2} : y^{2}$

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