A) \[3\sqrt{5}\]
B) 105
C) \[21\sqrt{5}\]
D) \[3\sqrt{45}\]
Correct Answer: C
Solution :
[c] \[{{y}^{4}}+\frac{1}{{{y}^{4}}}=47\] \[\Rightarrow {{y}^{4}}+\frac{1}{{{y}^{4}}}+2=49\,or\,{{\left( {{y}^{2}}+\frac{1}{{{y}^{2}}} \right)}^{2}}={{7}^{2}}\] \[\therefore \,\,{{y}^{2}}+\frac{1}{{{y}^{2}}}=7.....(i)\] Also, \[{{y}^{4}}+\frac{1}{{{y}^{4}}}-2-=45\] \[\Rightarrow \left( {{y}^{2}}-\frac{1}{{{y}^{2}}} \right)=\sqrt{45}=3\sqrt{5}\] \[\therefore \left( {{y}^{2}}+\frac{1}{{{y}^{2}}} \right)\left( {{y}^{2}}-\frac{1}{{{y}^{2}}} \right)=7\times 3\sqrt{5}\] \[{{y}^{4}}-\frac{1}{{{y}^{4}}}=21\sqrt{5}\]
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