Find the set E of the values of x for which the binomial expansion $(2 + 5 x)^{- 1 / 2}$ is valid.

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Solution

$(2 + 5 x)^{- 1 / 2} = 2^{- 1 / 2} (1 + \frac{5 x}{2})^{- 1 / 2}$
$∣ ∣ ∣ \frac{5 x}{2} ∣ ∣ ∣ < 1 ⟹ | x | < \frac{2}{5} ⟹ x \in (- \frac{2}{5}, \frac{2}{5})$

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