Question

What two numbers have a product of 18 and a sum of 11?​

Answer 1

Answer:

9 & 2

Explanation:

Answer 2

Answer: 2 and 9

2*9 = 18

2+9 = 11

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Explanation:

You can find this through trial-and-error. You're basically looking for factors of 18 which add to 11. Something like 6 and 3 won't work since 6+3 = 9, but 2 and 9 works since 2+9 = 11.

Or you can use algebra as shown below.

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Let x and y be the two numbers. They have a product of 18, so x*y = 18.

They also have a sum of 11, meaning x+y = 11. Solving for y leads to y = 11-x

Plug this into xy = 18 and we get x(11-x) = 18 which becomes -x^2+11x = 18

Now subtract 18 from both sides to arrive at the equation -x^2+11x-18 = 0.

Let's use the quadratic formula to solve.

We'll plug in a = -1, b = 11, c = -18

$x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(11)\pm\sqrt{(11)^2-4(-1)(-18)}}{2(-1)}\\\\x = \frac{-11\pm\sqrt{49}}{-2}\\\\x = \frac{-11\pm7}{-2}\\\\x = \frac{-11+7}{-2}\ \text{ or } \ x = \frac{-11-7}{-2}\\\\x = \frac{-4}{-2}\ \text{ or } \ x = \frac{-18}{-2}\\\\x = 2\ \text{ or } \ x = 9$

If x = 2, then y = 11-x = 11-2 = 9

If x = 9, then y = 11-x = 11-9 = 2

Both values of x lead to the same pair of values overall, meaning that 2 and 9 are the two values we're after.

2*9 = 18

2+9 = 11