Rationalise the denominator and simplify: .

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Problem

Rationalise the denominator and simplify: 45−51/4\dfrac{4}{\sqrt{5}-5^{1/4}}. (a) 4(5−51/4)5−5\dfrac{4(\sqrt{5}-5^{1/4})}{5-\sqrt{5}} (b) 4(5+51/4)25−5\dfrac{4(\sqrt{5}+5^{1/4})}{25-\sqrt{5}} (c) 4(5+51/4)5−5\dfrac{4(\sqrt{5}+5^{1/4})}{5-\sqrt{5}} (d) 4(5+51/4)5+5\dfrac{4(\sqrt{5}+5^{1/4})}{5+\sqrt{5}}

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