What adds to get 17 and multiplies to get 20?

Answer 1

The two numbers that add to get 17 and multiply to get 20 are 5 and 12. This is because 5 + 12 = 17 and 5 x 12 = 20. These two numbers satisfy both conditions simultaneously, making them the correct pair.

Answer 2

Assume that the question requires two numbers to be found.

Label the numbers a and b.

Then ab = 20, so b = 20/a.

And, a + b = 17 .............substituting for b gives :-

a + 20/a = 17..................multiplying throughout by a, a2 + 20 = 17a.

Which we can re-write as, a2 - 17a + 20 = 0.

Using the quadratic formula leads to, a = [17 ± √209] / 2

Thus, a = 15.7284 and 1.2716.

So the answer is that one number is 15.7284 and the other number is 1.2716. (4dp)