Find two positive numbers whose difference is 11 and whose product is 1026.

Question

I do not understand this problem

Answer 1

the two numbers are x and x+11, their difference = x+11-x = 11

their product = x(x+11) = 1026

x(x+11) = 1026

expand the left side and subtract 1026 from both sides

x^2 +11x = 1026

x^2 + 11x - 1026 = 1026-1026

x^2 + 11x - 1026 = 0

use the quadratic formula (unless you stumble upon two factors (x+27)(x-38) = 0 by trial and error)

x = -b/2a + or - (1/2a)sqr(b^2 - 4ac) where a= 1, b=11, c=-1026

x = -11/2 + or - (1/2)sqr(121 + 4104) = -11/2 + 65/2 or -11/2-65/2

= 54/2 or -76/2

= 27 or - 38

x+11 = 38 or -27

the two number are either

27 and 38

or

-27 and -38

their difference is 11

their product = 1026