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find the two number listed, find two factors of the first number such that their product is the first number and their sum is the second number -10, 9

1 Answer

3 votes

Let's call those two factors a and b. So, we have:

a * b = -10

a + b = 9

From the second equation, we can isolate a:

a + b = 9

a + b - b = 9 - b

a = 9 - b

Now, we can use this expression for a in the first equation to find b:

a * b = -10

(9 - b) * b = -10

9b - b² = -10

-b² + 9b + 10 = 0

Notice that we found a second-degree equation. We can either solve it, or just try some pairs of values for a and b to find which one fits the problem.

Let's try integer numbers. The integer pairs of factors of -10 are:

• -1 and 10

,

• 1 and -10

,

• -2 and 5

,

• 2 and -5

Since the sum of the factors is 9, the only possible pair is -1 and 10:

-1 + 10 = 9

Therefore, the factors are -1 and 10.

User Celso Dantas
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