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If a, b, c and d are in proportion, prove that: (iii)

    \[({{\mathbf{a}}^{\mathbf{4}}}~+\text{ }{{\mathbf{c}}^{\mathbf{4}}}):\text{ }({{\mathbf{b}}^{\mathbf{4}}}~+\text{ }{{\mathbf{d}}^{\mathbf{4}}})\text{ }=\text{ }{{\mathbf{a}}^{\mathbf{2}}}{{\mathbf{c}}^{\mathbf{2}}}:\text{ }{{\mathbf{b}}^{\mathbf{2}}}{{\mathbf{d}}^{\mathbf{2}}}\]

(iv)

    \[\frac{{{a}^{2}}+ab}{{{c}^{2}}+cd}=\frac{{{b}^{2}}-2ab}{{{d}^{2}}-2cd}\]

Class 10 | Exercise 1 | ICSE | Maths | ML Aggarwal | Ratio and Proportion
If a, b, c and d are in proportion, prove that: (iii)

    \[({{\mathbf{a}}^{\mathbf{4}}}~+\text{ }{{\mathbf{c}}^{\mathbf{4}}}):\text{ }({{\mathbf{b}}^{\mathbf{4}}}~+\text{ }{{\mathbf{d}}^{\mathbf{4}}})\text{ }=\text{ }{{\mathbf{a}}^{\mathbf{2}}}{{\mathbf{c}}^{\mathbf{2}}}:\text{ }{{\mathbf{b}}^{\mathbf{2}}}{{\mathbf{d}}^{\mathbf{2}}}\]

(iv)

    \[\frac{{{a}^{2}}+ab}{{{c}^{2}}+cd}=\frac{{{b}^{2}}-2ab}{{{d}^{2}}-2cd}\]

It is given that

a, b, c, d are in proportion

Consider a/b = c/d = k

a = b, c = dk

(iii)

    \[({{a}^{4}}~+\text{ }{{c}^{4}}):\text{ }({{b}^{4}}~+\text{ }{{d}^{4}})\text{ }=\text{ }{{a}^{2}}{{c}^{2}}:\text{ }{{b}^{2}}{{d}^{2}}\]

We can write it as

Therefore, LHS = RHS.

Therefore, LHS = RHS.

i

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