How could I find x in this equation x^2-x+6 \equiv 0

Kymani Shepherd

Kymani Shepherd

Answered question

2022-04-23

How could I find x in this equation
x2x+60±mod9

Answer & Explanation

Litzy Fuentes

Litzy Fuentes

Beginner2022-04-24Added 22 answers

Step 1
Complete the square, noting 417 and 215±mod9
x2x+41x2x+71±mod9
(x21)21±mod9
x21±14
because 9y21=(y+1)(y1) means 9y+1 or 9y1
Since 3y+1 and 3y1 means 3(y+1)(y1)=2
which is clearly not so.

belamontern9i

belamontern9i

Beginner2022-04-25Added 19 answers

Step 1
If x2±mod3
there are no solutions because
(3k+2)23k2=9k2+3k+20±mod3
If x0±mod3, then x20±mod9, so the solutions are given by x+6±mod9, i.e x=9k+6
If x1±mod3, then x2x+6=9k2+6k+13k1+63k+6±mod9, so k+20±mod3, and the solutions are k=3j+1, or x=9j+4
So the solutions are 4,6 (mod 9)

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