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Is it possible to determine two numbers such that their sum is 16 and their product is 48?

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greyapple | Student | eNoter

Posted August 14, 2011 at 10:09 PM via web

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Is it possible to determine two numbers such that their sum is 16 and their product is 48?

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted August 14, 2011 at 10:13 PM (Answer #1)

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The sum of the two numbers is 16 and their product is 48. Let the numbers be A and B.

A + B = 16

A*B = 48

From the two equations we get

A*(16 - A) = 48

=> 16A - A^2 = 48

=> A^2 - 16A + 48 = 0

=> A^2 - 12A - 4A + 48 = 0

=> A(A - 12) - 4(A - 12) = 0

=> (A - 4)(A - 12) = 0

=> A = 4 and A = 12

The two required numbers are 4 and 12.

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