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If a, b, c are in continued proportion, prove that: \[\frac{p{{a}^{2}}+qab+r{{b}^{2}}}{p{{b}^{2}}+qbc+r{{c}^{2}}}=\frac{a}{c}\]
If a, b, c are in continued proportion, prove that: \[\frac{p{{a}^{2}}+qab+r{{b}^{2}}}{p{{b}^{2}}+qbc+r{{c}^{2}}}=\frac{a}{c}\]
Class 10 | Exercise 1 | ICSE | Maths | ML Aggarwal | Ratio and Proportion
If a, b, c are in continued proportion, prove that: \[\frac{p{{a}^{2}}+qab+r{{b}^{2}}}{p{{b}^{2}}+qbc+r{{c}^{2}}}=\frac{a}{c}\]

It is given that

a, b, c are in continued proportion

\[\frac{p{{a}^{2}}+qab+r{{b}^{2}}}{p{{b}^{2}}+qbc+r{{c}^{2}}}=\frac{a}{c}\]

Consider a/b = b/c = k

So we get

a = bk and b = ck ….. (1)

From equation (1)

a = (ck) k = \[c{{k}^{2}}\] and b = ck

We know that

Therefore, LHS = RHS.

i

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