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## Main Question or Discussion Point

**x^2 - 11x + 22 = 0**

the roots are x= 3 and x = 6

what's the base of the numbers?

the roots are x= 3 and x = 6

what's the base of the numbers?

ok what I've done is I found the roots in decimal system which are

**x1 = (11+sqrt(33))/2 and x2 = (11-sqrt(33)/2**

then I said x1 = 3 and x2 = 6 so we have

**3 = (11+sqrt(33)/2 <=> 6 = 11+sqrt(33) <=> -5 = sqrt(33) <=> 25 = 33 <=> 2b + 5 = 3b + 3 <=> b = 2**

im doing the same for the second root

**6 = (11-sqrt(33)/2 <=> 12 = 11 -sqrt(33) <=> 1 = -sqrt(33) <=> 1 = 33 <=> 1 = 3b + 3<=>**

3b = -2 <=> b = -2/3

3b = -2 <=> b = -2/3

i know that my method is wrong, the correct answer is 8 but that's what I thought would solve this problem, it's the first time that I see this kind of problem, so if anyone could guide me I would apreciate it