Question

2 factors that add to 6 but multiply to 60

Answer 1

Answer:

The short answer is there isn’t.

Start by writing each of these as an expression:

x * y = 60

x + y = 7

Next, solve each for the same variable; in this case, y:

(x * y) / x = 60 / x

.: y = 60 / x

(x + y) - x = 7 - x

.: y = 7 - x

Next, replace y of the second expression to the first

y = 60 / x & y = 7 - x

.: 7 - x = 60 / x

Now, solve for x:

(7 - x) * x = (60 / x) * x

.: x * 7 - x^2 = 60

This is quadratic, so write it in the form of ax2 + bx + x = 0

(-1)x^2 + (7)x + (-60) = 0

.: a = -1, b = 7, c = -60

Finally solve for b:

x = (-b +- sqrt(b^2 - 4*a*c)) / 2a

.: x = (-7 +- sqrt(7^2 - 4*-1*-60)) / (2 * -1)

.: x = (-7 +- sqrt(49 - 240)) / -2

.: x = (-7 +- sqrt(-191)) / -2

The square root of a negative value is imaginary and thus there’s no real answer to this problem.