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Mathematics
Mira Kerr
4 June, 05:12
Product 48 and sum 14 what are the factors
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Roselyn Webster
4 June, 07:22
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6 and 8
6*8 = 48
6+8 = 14
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Maximus Mcpherson
4 June, 07:51
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Step-by-step explanation:
Let's write a system.
Let's say that the variables are x and y.
xy=48
x+y=14
Solve for one of the variables, let's say, x.
x=14-y.
Now substitute x into the 1st equation.
(14-y) y=48
Simplify.
-y²+14y=48
Make it into a quadratic equation.
-y²+14y-48=0
Make sure y²'s coefficient is one. Divide everything by - 1
y²-14y+48=0
Now factor!
What factors add up to 14 and multiply to 48.
6 and 8!
Since the 2nd term is negative, and the 3rd term is positive, the factors have to be negative.
y²-6y-8y+48=0
Group.
(y²-6y) + (-8y+48) = 0
y (y-6) - 8 (y-6) = 0
(y-8) (y-6) = 0
y-8=0
y-6=0
y=8 y=6
now let's substitute each y value into y²-14y+48=0
8²-14 (8) + 48=0
64-112+48=0
0=0. so y=8 checks out!
6²-14 (6) + 48=0
36-84+48=0
0=0 so y=6 also checks out!
Choose one y value and solve for x, in each equation:
xy=48
x+y=14
8x=48
x+8=14
x=6
x=6
It checks out!
so the factors are
x=6 y=8.
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