uptetd16p1 q105

105The sum and multiplication of two numbers are 11 and 18 respectively, then the sum of their reciprocals is

A
B
C
D

Option : D
Explanation : Sum of two numbers is 11.
∴ Let the two numbers be x and (11 - x)
According to the question, x(11 - x) = 18
⇒ -x² + 11x = 18
⇒ x² - 11x + 18 = 0
⇒ x² - 9x - 2x + 18 = 0
⇒ x(x - 9) - 2(x - 9) = 0
⇒ (x - 2)(x - 9) = 0
⇒ x = 2, 9
Thus, the two numbers are 2 and 9

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