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Heath Smitham
Wiki User
∙ 11y agoSince 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)
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