1.

The product of two numbers is 48 and their sum is 16.Find the numbers

Answer»

LET the two numbers be x and y


Given that, x + y = 16 and xy = 48


xy = 48, => x = 48 / y


Substituting x = 48 / y in the equation x + y = 16, we GET,


48 / y + y = 16


Taking LCM,


48 + y² / y = 16


48 + y² = 16 y


=> y² - 16y + 48 = 0


=> y² - 12 y - 4 y + 48 = 0


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


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


=> y = 4, 12


If y = 4, then x = 48 / 4 = 12


If y = 12, then x = 48 / 12 = 4


Hence the two numbers just get INTERCHANGED in both cases. Hence the two numbers are 12 and 4.


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