Find the value of $(2^{1 / 4} - 1) (2^{3 / 4} + 2^{1 / 2} + 2^{1 / 4} + 1)$ .

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Solution

Put $2^{1 / 4} = x$
$\Rightarrow$ Given expression $= (x - 1) (x^{3} + x^{2} + x + 1)$
$= x^{4} - 1$
$= {(2^{1 / 4})}^{4} - 1 = 2 - 1 = 1$

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