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What 2 numbers multiply to get 522 and add to get -180

User EagleFox
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1 Answer

11 votes

Answer:

  • -2.94829122872 = -90 +3√842
  • -177.05170877128 = -90 -3√842

Explanation:

You want two numbers that have a product of 522 and a sum of -180.

Equations

The requirements can be written as the equations ...

x + y = -180

xy = 522

Solution

The first can be used to write an expression for y:

y = -180 -x

Substituted into the second equation, we have ...

x(-180 -x) = 522

x² +180x = -522 . . . . . eliminate parentheses, multiply by -1

x² +180x +8100 = 8100 -522 . . . . . complete the square

(x +90)² = 7578

x = -90 ± 3√842 . . . . . take the square root, add -90

y = -x -180 = -90 ± 3√842 . . . . . . sign opposite that of x

The two numbers are irrational:

  • -2.94829122872 = -90 +3√842
  • -177.05170877128 = -90 -3√842

__

Additional comment

Factor pairs of 522 are ...

522 = 1×522 = 2×261 = 3×174 = 6×87 = 9×58 = 18×29

Sums of these pairs are 523, 263, 177, 93, 67, 47. The closest sum to 180 is 177 = 174 + 3.

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What 2 numbers multiply to get 522 and add to get -180-example-1
User Phillip Elm
by
8.2k points

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