If \( \frac{a}{b}=\frac{b}{c}=\frac{c}{d} \), prove that \( \frac{a}{d} \) is equal to \( \sqrt{...

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If \( \frac{a}{b}=\frac{b}{c}=\frac{c}{d} \), prove that \( \frac{a}{d} \) is equal to \( \sqrt{\frac{a^{5}+b^{2} c^{2}+a^{3} c^{2}}{b^{4} c+d^{4}+b^{2} c d^{2}}} \)
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