Question

The difference between two positive numbers is 4 and the difference between their cubes is 316 . find their product and the sum of their square . plz ans this step by step

Answer 1

let the numbers be x an y
we have. x-y=4 ,x^3-y^3= 316
now,
x-y=4
cubing on both the sides
(x-y)^3=4^3
x^3-y^3-3xy(x-y)=64
316-3xy(4)=64
316-3xy=64/4
316-3xy=16
-3xy=16-316
-3xy=-300
xy=-300/-3
xy=100
now,
x-y=4
(x-y)^2=4^2
x^2+y^2-2xy=16
x^2+y^2-2*100=16
x^2+y^2-200=16
x^2+y^2=16 +200
x^2+y^2=216

hope it helps