Question

The product of two numbers is 144, but their sum is -24. What are these two numbers?

Answer 1

The two numbers are - 12 and - 12 .

Explanation:

Let the two numbers be x and y then

By the question

x * y = 144

or x = 144 / y ....... I)

Again

x + y = - 24

Or 144/y + y = - 24

or, ( 144 + y²) / y = - 24

or, 144 + y² = - 24y

y² + 24y + 144 = 0

y² + ( 12 + 12 ) y + 144 =0

y² + 12y + 12y + 144 = 0

y(y + 12 ) + 12 ( y + 14) = 0

( y + 12 ) ( y + 12 ) = 0

Either

y + 12 =0

y = - 12

Now

x = 144 / - 12 = - 12

Therefore the two numbers are - 12 and - 12 .

Hope it will help :)❤