A) \[\frac{-\,5}{4}\]
B) \[\frac{5}{4}\]
C) \[\frac{1}{4}\]
D) \[\frac{-\,1}{4}\]
Correct Answer: B
Solution :
\[\because \] \[\sqrt{1-\sqrt{{{x}^{4}}-{{x}^{2}}}}=x-1\] Or \[1-\sqrt{{{x}^{4}}-{{x}^{2}}}={{(x-1)}^{2}}\] Or \[1-\sqrt{{{x}^{4}}-{{x}^{2}}}=({{x}^{2}}-2x+1)\] Or \[-\sqrt{{{x}^{4}}-{{x}^{2}}}=({{x}^{2}}-2x)\] Or \[{{x}^{4}}-{{x}^{2}}={{({{x}^{2}}-2x)}^{2}}\] Or \[{{x}^{4}}-{{x}^{2}}={{x}^{4}}+4{{x}^{2}}-4{{x}^{3}}\] Or \[4{{x}^{3}}-{{x}^{2}}-4{{x}^{2}}=0\] Or \[4{{x}^{3}}-5{{x}^{2}}=0\] Or \[{{x}^{2}}(4x-5)=0\] Or \[x=0,\] \[\frac{5}{4}\]
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