Two positive numbers x and y are such that x>y. If the difference of these numbers is 5 and their product is 24, find sum of these numbers.
A
16
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B
11
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C
19
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D
32
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Solution
The correct option is B11 Given, x>y Thus, x−y=5 and xy=24 x−y=5 Squaring both sides, =>(x−y)2=52 =>x2+y2−2xy=25 =>x2+y2=25+2(24) =>x2+y2=73 Now, (x+y)2=x2+y2+2xy =73+2(24) =73+48 =121 =>x+y=√121 =±11 Given, x and y are positive numbers, Therefore, x+y=11