Question

If product of 2 numbers is 120 and sum of their squares is 289. Then the sum of the number is ?

Answer 1

Let first number be x and the second number be y.

Therefore,

xy = 120
x ^ 2 + y ^ 2 = 289

We will use a very frequently used identity which is as follows:

( x + y ) ^ 2 = x ^ 2 + y ^ 2 + 2xy

Substituting the values we know,

( x + y ) ^ 2 = 289 + 2 * 120
( x + y ) ^ 2 = 289 + 240
( x + y ) ^ 2 = 529
( x + y ) = √529

Hence,

x + y = 23

Therefore,

The sum of the numbers will be 23.

Answer 2

Here is your solution

Given :-

product of 2 numbers is 120

sum of their squares is 289.

Let

Number be x and y.

so

A/q

=>xy = 120

=>x^2 + y^2 = 289

Now We will use identity:-

( x + y ) ^ 2 = x ^ 2 + y ^ 2 + 2xy

Putting the values

(x + y)^2 = 289 + 2×120
(x + y)^2 = 289 + 240
(x + y)^2 = 529
(x + y) = √529

x + y = 23✔

Hence

The sum of the numbers is 23.

Hope it helps you