A) \[ab=dc\]
B) \[ac=bd\]
C) \[ad+bc=0\]
D) \[\frac{a}{b}=\frac{c}{d}\]
Correct Answer: D
Solution :
Accordingly, \[{{\{2(ac+bd)\}}^{2}}=4({{a}^{2}}+{{b}^{2}})({{c}^{2}}+{{d}^{2}})\] Þ \[4{{a}^{2}}{{c}^{2}}+4{{b}^{2}}{{d}^{2}}+8abcd=4{{a}^{2}}{{c}^{2}}+4{{a}^{2}}{{d}^{2}}\] \[+4{{b}^{2}}{{c}^{2}}+4{{b}^{2}}{{d}^{2}}\] Þ \[4{{a}^{2}}{{d}^{2}}+4{{b}^{2}}{{c}^{2}}-8abcd=0\,\,\,\Rightarrow 4{{(ad-bc)}^{2}}=0\] Þ \[ad=bc\Rightarrow \frac{a}{b}=\frac{c}{d}\].You need to login to perform this action.
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