Answer:
The numbers are 72 and 96.
Step-by-step explanation:
LCM + GCF = 312
LCM - GCF = 264
2*LCM = 576
LCM = 576/2 = 288
HCF = 312–288 = 24
The product of two numbers = HCF*LCM
Let the numbers be x and (168-x)
x(168-x) = 24*288 = 6912
x^2–168x+6912 = 0
x = [168 +(168^2 -4*6912)^0.5]/2
= [168 +(28224–27648)^0.5]/2
= [168 + 576^0.5]/2
= (168+24}/2
= 192/2
= 96 and the other number is 168–96 = 72.
