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If a, b, c and d are in proportion, prove that: (v)\[\frac{{{(a+c)}^{3}}}{{{(b+d)}^{3}}}=\frac{a{{(a-c)}^{2}}}{b{{(b-d)}^{2}}}\] (vi) \[\frac{{{a}^{2}}+ab+{{b}^{2}}}{{{a}^{2}}-ab+{{b}^{2}}}=\frac{{{c}^{2}}+cd+{{d}^{2}}}{{{c}^{2}}-cd+{{d}^{2}}}\]
If a, b, c and d are in proportion, prove that: (v)\[\frac{{{(a+c)}^{3}}}{{{(b+d)}^{3}}}=\frac{a{{(a-c)}^{2}}}{b{{(b-d)}^{2}}}\] (vi) \[\frac{{{a}^{2}}+ab+{{b}^{2}}}{{{a}^{2}}-ab+{{b}^{2}}}=\frac{{{c}^{2}}+cd+{{d}^{2}}}{{{c}^{2}}-cd+{{d}^{2}}}\]
Class 10 | Exercise 1 | ICSE | Maths | ML Aggarwal | Ratio and Proportion
If a, b, c and d are in proportion, prove that: (v)\[\frac{{{(a+c)}^{3}}}{{{(b+d)}^{3}}}=\frac{a{{(a-c)}^{2}}}{b{{(b-d)}^{2}}}\] (vi) \[\frac{{{a}^{2}}+ab+{{b}^{2}}}{{{a}^{2}}-ab+{{b}^{2}}}=\frac{{{c}^{2}}+cd+{{d}^{2}}}{{{c}^{2}}-cd+{{d}^{2}}}\]

It is given that

a, b, c, d are in proportion

Consider a/b = c/d = k

a = b, c = dk

Therefore, LHS = RHS.

Therefore, LHS = RHS.

i

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