What two numbers multiply to 1600 and add to 60?

Answer 1

Let the numbers be x and y, then

x + y = 60 (which yields y = 60 - x)

xy = 1600 (replace y with 60 - x)

x(60 - x) = 1600

60x - x2 = 1600 (multiply by -1 to both sides)

x2 - 60x = -1600 (add 302 to both sides to complete the square)

x2 - 60x + 302 = -1600 + 900

(x - 30)2 = -700 (take the square root of both sides)

x - 30 = ± √-700 (add 30 to both sides and write -700 = (100)(7)(-1))

x = 30 ± (√100)(√7)(√-1)

x = 30 ± (10√7)i

So,

x = 30 + (10√7)i or x = 30 - (10√7)i

thus,

y = 60 - [30 + (10√7)i] or y = 60 - [30 - (10√7)i ]

y = 30 - (10√7)i or y = 30 + (10√7)i

Therefore,

[30 + (10√7)i] + [30 - (10√7)i] = 60

[30 + (10√7)i] [30 - (10√7)i] = 1600

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