SOLUTION: Find two numbers which add to give -1 and multiply to give -20.

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Question 1178330: Find two numbers which add to give -1 and multiply to give -20.

Found 4 solutions by mananth, ikleyn, greenestamps, josgarithmetic:
Answer by mananth(16946)   (Show Source):
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let the numbers be x & y
x+y=-1
x*y = -20
x=-20/y
x+y=-1
-20/y +y =-1
-20 +y^2 =-y
y^2+y-20=0
(y+5)(y-4)=0
y=5,-4
x=4,-5

Answer by ikleyn(52752)   (Show Source):
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.

In the post by @Mananth, the answer is presented in absurdist form.

The correct answer in correct form is THIS:

The numbers are 4 and -5.

Answer by greenestamps(13195)   (Show Source):
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x+y = -1
xy = -20

Solve the first equation for one variable and substitute in the second equation.

y = -1-x
x(-1-x) = -20
-x-x^2 = -20
x^2+x-20 = 0
(x+5)(x-4) = 0
x = -5 or x = 4

If x = -5 then y = 4; if x = 4 then y = -5. Either way, the two numbers are -5 and 4.

That's a nice exercise in using basic algebra to solve the problem. But using formal algebra on this problem is overkill. Solve the problem using logical reasoning and simple mental arithmetic.

The product of the two numbers is negative, so we know one is positive and one is negative.
Now ignore the signs for the moment; then we need two numbers whose product is 20 and whose difference is 1. It takes about one second to find those numbers are 4 and 5.
Now make one of them positive and the other negative so that their sum is -1.

ANSWERS: -5 and 4.

Answer by josgarithmetic(39613)   (Show Source):
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and
;

The only way the two numbers can add to become -1 is the larger factor is the negative factor.

check:

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