If $$ \mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d} $$ are in continued proportion , prove that $$ : \frac{\mathrm{ab}-\mathrm{cd}}{\mathrm{b}^{2}-\mathrm{c}^{2}}=\frac{\mathrm{a}+\mathrm{c}}{\mathrm{b}} $$

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Knight Murphy · Accepted Answer

To prove the statement, we use the definition of continued proportion, $$ \frac{a}{b} = \frac{c}{d} $$, which implies $$ ad = bc $$. We then manipulate the expressions $$ ab - cd $$ and $$ b^2 - c^2 $$ to show that they are equivalent to $$ \frac{a + c}{b} $$.

If \( \mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d} \) are in continued proportion , prove that \( : \frac{\mathrm{ab}-\mathrm{cd}}{\mathrm{b}^{2}-\mathrm{c}^{2}}=\frac{\mathrm{a}+\mathrm{c}}{\mathrm{b}} \)

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If \( \mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d} \) are in continued proportion , prove that \( : \frac{\mathrm{ab}-\mathrm{cd}}{\mathrm{b}^{2}-\mathrm{c}^{2}}=\frac{\mathrm{a}+\mathrm{c}}{\mathrm{b}} \)

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