Mathematics in the Modern World

Question

Two numbers have a difference of five, and their product is 84. what is the sum of the number?

Answer 1

x-y -5

xy=84

y=84/x

x-84/x =5

x^2-84 =5x

x^2-5x -84=0

x= 5/2 +/- (1/2)sqr(25+336)= 2.5+/-.5sqr361

x= 2.5+/-9.5 = -7, 12

y = -12, 7

or factor

(x+7)(x-12)=0

x=-7, 12

y=-12, 7

the two numbers sum to -19 or +19