Question

the product of two numbers is 24 and the sum of their squares is 52 find their sum​

Answer 1

Let the numbers be x and y

xy = 24

x^2 + y^2 = 52

So

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

(x+y)^2 = 52 + 48

(x+y)^2 = 100

x + y = 10

So their sum is 10.

Answer 2

Step-by-step explanation:

Let the two numbers be x and y.

As per question,

x X y = 24

x = 24 / y

x² + y² = 54

(24/y)² + y² = 54

576 / y² + y² = 54

576 + y^4 = 54 y²

y^4 - 52 y^2 + 576 = 0

y^2 = 52 + 20 / 2 = 36

y = 6

Now,

x = 24/6 = 4

Hence, sum of the two numbers = 6 + 4 = 10

Hope it helps.