The product (X) of two numbers is 24 and their sum (+) is 10. What is the value of the largest of the two numbers?

let the two numbers be x and y

From the first sentence

xy=24 ... (1)

x+y=10 ... (2)

from equation 2 make y the subject of the formular and substitute it in equation 1

y=10-x

in equation one

x (10-x) = 24

10x-x^2=24

=-x^2+10x=24

transfer the constant 24 to the left hand side and equate it to 0

=-x^2+10x-24=0

Then factorise completely