How could I find x in this equation

Javion Kerr

Javion Kerr

Answered question

2022-03-25

How could I find x in this equation
x2-x+60(mod9)

Answer & Explanation

zalutaloj9a0f

zalutaloj9a0f

Beginner2022-03-26Added 17 answers

Step 1
Complete the square, noting 417 and 2-15(mod9)
x2-x+4-1x2-x+71(mod9)
(x-2-1)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.

Theodore Davila

Theodore Davila

Beginner2022-03-27Added 14 answers

Step 1
If x2(mod3)
there are no solutions because
(3k+2)2-3k-2=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 x2-x+6=9k2+6k+1-3k-1+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)

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?