High School

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------------------------------------------------ diamond problem for -2 and -5

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Answer :

Step-by-step explanation:

if I understand you correctly, then let's call the missing numbers l, r (for left and right).

and

-2 = l × r

-5 = l + r

l = -r - 5

therefore,

-2 = (-r - 5) × r = -r² - 5r

that gives us the quadratic equation

-r² - 5r + 2 = 0

for the general solutions

x = (-b ± sqrt(b² - 4ac))/(2a)

we have here

a = -1

b = -5

c = 2

and x = r, of course

r = (5 ± sqrt(25 - 4×-1×2))/(2×-1) =

= (5 ± sqrt(25 + 8))/-2 = (5 ± sqrt(33))/-2

r1 = (5 + sqrt(33))/-2 = -5.372281323...

r2 = (5 - sqrt(33))/-2 = 0.372281323...

as l = -r - 5, we see that r1 = l2, and r2 = l1.

but these are the only solutions.

there are no integer number solutions.