BenoguigoliB

2021-03-15

Find a complete set of mutually incogruent solutions.

$9x\equiv 12\pm od\left\{15\right\}$

lobeflepnoumni

Skilled2021-03-17Added 99 answers

Step 1

Since 15 is not prime number .Prime factorization of 15 is$5\times 3$ . Convert the given equation in $b\text{mod}5$ and mod 3.

The solution of the equation$9x\equiv 12\pm od3$ and

$9x\equiv 12\pm od5$

Now solve the above system that will be find out by finding common solution of above equations.

Step 2

Solve the equation$9x\equiv 12\pm od3$ .

The equivalent meaning of above equation is$\frac{3}{9x}-12$ that is $\frac{3}{3}(3x-4)$ . Since 3 divide 9x−12 always inn-respective of values of $x\in \mathbb{Z}$ . Therefore solution of equation is $\mathbb{Z}$ .

Now solve the equation$9x\equiv 12\pm od5$ .

$9x\equiv 12\pm od5$

$4x\equiv 2\pm od5$

$-x\equiv 2\pm od5$

$x\equiv -2\pm od5$

$x\equiv 3\pm od5$

The solution of the equation$x\equiv 3\pm od5$ is 5k+3 where k is an integer. The common solution of both the equation is 5k+3 where k is an integer.

The set form of the solution is$\le ft\{5k+3.k\in \mathbb{Z}right\}$ .

Since 15 is not prime number .Prime factorization of 15 is

The solution of the equation

Now solve the above system that will be find out by finding common solution of above equations.

Step 2

Solve the equation

The equivalent meaning of above equation is

Now solve the equation

The solution of the equation

The set form of the solution is

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