What two numbers multiply to 42 and add to make 1?

Answer 1

43

Answer 2

Since the product of two numbers is 42 and the sum of two numbers is 1, we have:

xy = 42

x + y = 1

Solve this system of equations by substitution!

First, solve for y:

y = 42/x

Substitute that equation for the second equation:

x + (42/x) = 1

Solve for x!

x² + 42 = x

x² - x + 42 = 0

Complete the squares!

x² - x + (-½)² = -42 + (-½)²

(x - ½)² = -42 + ¼

(x - ½)² = -167/4

So...

x = (1 ± i√167)/2

Therefore, there are no real numbers that multiply to get 42 and add altogether to get 1.

The imaginary numbers that give these values are:

x = ½(1 - i√167) and y = ½(1 + i√167)

x = ½(1 + i√167) and y = ½(1 - i√167)