Question

Find two numbers whose sum is 54 and whose product is 585

Answer 1

let first number be x and second be y

x + y=54.....................................eq1 , x=54-y

xy = 585......................................eq2

(54-y)y = 585

y² - 54y + 585=0

After solving the above quadratic equation we get x=39,y=15 or x=15,y=39

Alternate Solution

You can just think of two numbers which after multiplying will give 5 in the unit place

Only both the numbers having unit digit 5 or one number having unit digit 5 and other having unit digit 9 can give you 5 in unit place after multiplying.

Eg : 5 * 5=25 (5 in unit place)

15 * 15=225 (5 in unit place)

9 * 5=45 (5 in unit place)

19 * 5=95 (5 in unit place)

Now,we are given x+y=54 and xy=585

take any two numbers from 0 to 54 having 9 or 5 in unit place which when added will give 54 and 585 when multiplied.Hit and Trial method

Suppose we chose 49 and 5 both numbers have 5 or 9 in their unit place and both give 54 when added but their multiplication will yield 245 and not 585

Now chose another set of numbers say we chose 39 and 15 which give 54 when added and surprisingly give 585 when multiplied.

So,it can also be solved by hit and trial method