What two numbers have a product of -2 and a sum of 7

Mathematics

1 answer:

Citrus2011 [14]3 years ago

7 0

<em>Greetings from Brasil...</em>

According to the statement of the question, we can assemble the following system of equation:

X · Y = - 2 i

X + Y = 7 ii

isolating X from i and replacing in ii:

X · Y = - 2

X = - 2/Y

X + Y = 7

(- 2/Y) + Y = 7 <em>multiplying everything by Y</em>

(- 2Y/Y) + Y·Y = 7·Y

- 2 + Y² = 7X <em> rearranging everything</em>

Y² - 7X - 2 = 0 <em>2nd degree equation</em>

Δ = b² - 4·a·c

Δ = (- 7)² - 4·1·(- 2)

Δ = 49 + 8

Δ = 57

X = (- b ± √Δ)/2a

X' = (- (- 7) ± √57)/2·1

X' = (7 + √57)/2

X' = (7 - √57)/2

So, the numbers are:

and

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