A) \[\left( 1-\sqrt[4]{2} \right)\left( 2-\sqrt{2} \right)\]
B) \[\left( 1-\sqrt[4]{2} \right)\left( 2+\sqrt{2} \right)\]
C) \[-\left( 1+\sqrt[4]{2} \right)\left( 1+\sqrt{2} \right)\]
D) \[\left( 1+\sqrt[4]{2} \right)\left( 2+\sqrt{2} \right)\]
Correct Answer: C
Solution :
(c): \[\frac{1}{1-\sqrt[4]{2}}=\frac{1+\sqrt[4]{2}}{{{1}^{2}}-{{\left( \sqrt[4]{2} \right)}^{2}}}=\] \[\frac{1+\sqrt[4]{2}}{1-\sqrt{2}}=\frac{\left( 1+\sqrt[4]{2} \right)\left( 1+\sqrt{2} \right)}{-1}\]
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