A) \[ab\]
B) \[4ab\]
C) \[4({{a}^{2}}-{{b}^{2}})\]
D) \[4({{a}^{2}}+{{b}^{2}})\]
Correct Answer: C
Solution :
\[{{(x+iy)}^{1/3}}=a+ib\Rightarrow x+iy={{(a+ib)}^{3}}\] \[x+iy=({{a}^{3}}-3a{{b}^{2}})+i(3{{a}^{2}}b-{{b}^{2}})\] \[x={{a}^{3}}-3a{{b}^{2}},y=3{{a}^{2}}b-{{b}^{3}}\] \[\frac{x}{a}+\frac{y}{b}=\frac{{{a}^{3}}-3a{{b}^{2}}}{a}\div \frac{3{{a}^{2}}b-{{b}^{3}}}{b}\] \[={{a}^{2}}-3{{b}^{2}}+3{{a}^{2}}-{{b}^{2}}\] \[=4{{a}^{2}}-4{{b}^{2}}\Rightarrow 4({{a}^{2}}-{{b}^{2}})\]
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