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Oh, dude, that's like basic math, right? So, if you think about it, you need two numbers that when you add them, you get 6, and when you multiply them, you get 24. It's like a puzzle for toddlers, but hey, the numbers you're looking for are 4 and 6. So, 4 + 6 = 10, and 4 x 6 = 24. Math is fun, right?
Well, isn't that just a happy little puzzle! The numbers that add up to 6 and multiply to 24 are 3 and 4. You see, 3 plus 4 equals 7, and 3 times 4 equals 12, which are close but not quite there. So, let's try 2 and 12 instead. Two plus twelve equals 14, and two times twelve equals 24! Happy little numbers, just like that.
m + n = 6
mn = 24
Hence m = 24/n
Substitute
24/n + n = 6
Multiply through by 'n'
24 + n^2 = 6n
n^2 - 6n + 24 = -0
This does NOT factor so apply the Quadratic Equation.
n ={--6+/- sqrt[(-6)^2 - 4(1)(24)]} / 2(1)
n = {6 +/- sqrt[36 - 96]} / 2
n = {6 +/- sqrt[-60]} / 2
We now move into imaginary numbers, designated by 'i' (= sqrt(-1) .
Hence
n = {6 +/- i sqrt(60)} / 2
n = {6 +/- i(7.74596...)} / 2
n = 3 +/- 3.87298... i
Hence n = 3 + 3.87298...i & 3 - 3.87298 ... i
The two numbers that add up to 6 and multiply to 24 are 3 and 8. This is because 3 + 8 = 11 and 3 * 8 = 24. These two numbers satisfy both conditions simultaneously.
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What multiplies into 24 and adds up to -10?
14
What multiplies to 18 and adds to 6?
24
What adds up to 7 and multiplies to 6?
6*1
What adds up to -7 and multiplies to 6?
-6 and -1.
What multiplies to 36 and adds up to -12?
It is: -6 and -6
What multiplies to -12 and adds up to -4?
-16
What multiplies to 24 but adds to 2?
26
What adds up to -6 but multiplies to 9?
-3 and -3
What adds up to -3 and multiplies to -18?
-21
What multiplies into negative 48 and adds up to 2?
50
What adds up to -4 and multiplies to -24?
-28
What multiplies to 6 and adds to 7?
6 and 1
