If x, y and z are in continued proportion then prove that $z : x :: z^{2} : y^{2}$ . [2 Marks]

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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, $z y^{2} = x z^{2}$ [1 Mark]
$⟹$ $(z / x) = (z^{2} / y^{2})$
$⟹$ $z : x :: z^{2} : y^{2}$ [1 Mark]

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