Question

if a,b,c,and d are proportional then find b^2+d^2/a^2+c^2​

Answer 1

Hey mate here is ur
Given a,b,c,d are in proportional
therefore
$\frac{a}{b} = \frac{c}{d} = k(say) \\ a = bk \: and \: c = dk$
$put \: these \: values \: in \: \frac{ {b}^{2} + {d}^{2} }{ {a}^{2} + {c}^{2} } \\ = \frac{ {b}^{2} + {d}^{2} }{ {(bk)}^{2} + {(dk)}^{2} } \\ = \frac{ {b}^{2} + {d}^{2} }{ {b}^{2} {k}^{2} + {d }^{2} {k}^{2} } \\ = \frac{ {b}^{2} + {d}^{2} }{ {k}^{2} ( {b}^{2} + {d}^{2}) } \\ = \frac{1}{ {k}^{2} }$
Hope this hepls u
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