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Question

The sum of two numbers is 48 and their product is 432 Find the numbers.

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Solution

Let the two numbers be x and y,

x + y =48

xy = 432

Let these numbers be roots of equation. The equation will be :
p squared minus left parenthesis x plus y right parenthesis p plus x y equals 0
p squared minus 48 p plus 432 equals 0 p squared minus 16 p minus 12 p plus 432 equals 0 p left parenthesis p minus 16 right parenthesis minus 12 left parenthesis p minus 16 right parenthesis equals 0 left parenthesis p minus 12 right parenthesis left parenthesis p minus 16 right parenthesis equals 0 p equals 16 comma 12
So the two numbers are 16 and 12

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