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Question -

The sum of two numbers is 9. The sum of their reciprocals is 1/2. Find the numbers. [CBSE 2012]



Answer -

Sum of two numbers = 9
Let first number = x
Then second number = 9 тАУ x
According to the condition,
┬а
By cross multiplication
18 = 9x тАУ x2
=> x2 тАУ 9x + 18 = 0
=> x2 тАУ 6x тАУ 3x + 18 = 0
=> x (x тАУ 6) тАУ 3 (x тАУ 6) = 0
=> (x тАУ 6) (x тАУ 3) = 0
Either x тАУ 6 = 0, then x = 6
or x тАУ 3 = 0, then x = 3
Numbers are 6 and (9 тАУ 6) = 3, or 3 and (9 тАУ 3) = 6
Numbers are 3, 6

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