a^-1/2 = 3 - (1/a^{- 1/2}) হলে √a - (1/√a) = কত?

প্রশ্ন: a^-1/2 = 3 - (1/a^{- 1/2}) হলে √a - (1/√a) = কত?

সমাধান:
দেওয়া আছে,
a^-1/2 = 3 - (1/a^{- 1/2})
⇒ 1/√a = 3 - √a
⇒ √a + (1/√a) = 3

এখন,
{√a - (1/√a)}² = {√a + (1/√a)}² - 4 ⋅ √a ⋅ (1/√a)
= 3² - 4
= 9 - 4
= 5
∴ √a - (1/√a) = √5