The sum of a number and its reciprocal is 17/4. Find the number.
Let the number be a.
⇒ a + 1/a = 17/4
⇒ 4a2 + 4 – 17a = 0
⇒ 4a2 – 16a – a + 4 = 0
⇒ 4a(a – 4) –(a – 4) = 0
⇒ (4a – 1)(a – 4) = 0
⇒ a = 1/4 or 4