the difference between a positive fraction and its reciprocal is 9/20 find the sum of that fraction and its reciprocal.
Choose the correct choice from the following options:	A) 41/20	B) 17/20	C) 11/20	D) 9/20	E) None of these
Explanation :   Let the fraction = x   Then x − (1/x) = 9/20   ⇒ (x2 − 1)/x = 9/20   ⇒ x2 − 1 = 9x/20   ⇒ 20x2 − 20 = 9x   ⇒ 20x2 − 9x − 20 = 0   x=−b±b2−4ac√2ax=−b±b2−4ac2a =9±(−9)2−4×20×(−20)√2×20=9±(−9)2−4×20×(−20)2×20 =9±81+1600√40=9±4140=5040Or−3240=9±81+160040=9±4140=5040Or−3240   Given that the fraction is positive. Hence   x = 50/40 = 5/4   1/x = 4/5   x + (1/x) = (5/4) + (4/5) = (5 × 5 + 4 × 4)/20 = 41/20. 41/20nswer : Option 41/20
<result>A</result>
the difference between a positive fraction and its reciprocal is 9/20 find the sum of that fraction and its reciprocal.