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labwork [276]
3 years ago
8

What are two numbers multiplied together to get 15 but add to be 12?

Mathematics
1 answer:
KiRa [710]3 years ago
3 0
So x times y=15
x+y=12
solve
x+y=12
subtract x from both sides
y=12-x
subsitute
xy=15
x(12-x)=15
distribute
12x-x^2=15
subtract (12x-x^2) from both sides
0=x^2-12x+15
use quadratic formula which is
x=\frac{ -b+/- \sqrt{b^{2}-4ac} }{2a}
where you have
0=ax^2+bx+c
so
a=1
b=-12
c=15
subsitute
x=\frac{ -(-12)+/- \sqrt{-12^{2}-4(1)(15)} }{2(1)}
x=\frac{ 12+/- \sqrt{144-60} }{2}
x=\frac{ 12+/- \sqrt{84} }{2}
x=\frac{ 12+/- 2\sqrt{21} }{2}
x=6+/- \sqrt{21}
x=6+ \sqrt{21} or 6- \sqrt{21} or aprox
x=10.5826 or 1.41742
the numbers are 10.5826 and 1.41742






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