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4 years ago

What two numbers multiply and get 100 and add and get -29??

2 answers:

6 0

X, y - the numbers

The numbers multiply to 100.
$xy=100$

The numbers add up to -29.
$x+y=-29 \\
y=-x-29$

Substitute -x-29 for y in the first equation:
$x(-x-29)=100 \\
-x^2-29x=100 \\
-x^2-29x-100=0 \\
-x^2-4x-25x-100=0 \\
-x(x+4)-25(x+4)=0 \\
(-x-25)(x+4)=0 \\
-x-25=0 \ \lor \ x+4=0 \\
x=-25 \ \lor \ x=-4 \\ \\
y=-x-29 \\
y=-(-25)-29 \ \lor \ y=-(-4)-29 \\
y=25-29 \ \lor \ y=4-29 \\
y=-4 \ \lor \ y=-25 \\ \\
(x,y)=(-25,-4) \hbox{ or } (x,y)=(-4,-25)$

The numbers are -4 and -25.

rodikova [14]4 years ago

5 0

I simply start by writing the possible factors of 100
1x100
2x50
4x25 this is the correct combination
therefore -25 x - 4= 100
-25+ -4= -29

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