What two numbers add up to 72 and multiply to 1296?

Answer 1

1368

Answer 2

Let the two numbers be x & y:

• x + y = 72
• x * y = 1296

rearrange the first equation so [y = 72 - x], and substitute this into the second equation:

• x * (72 - x) = 1296 ---> 72*x - x² = 1296 ---> 0 = x² - 72x + 1296

Now use the quadratic equation: x = (72 +/- sqrt(72² - 4*1*1296))/2 = 72/2 = 36.

So 36 + y = 72 : y = 36. and this satisfies the second equation: 36*36 = 1296.

So x = y = 36.