Quadratic equation, linear equation in Modular Arithmetic in Hausa

Описание: Quadratic equation and expansion in Modular Arithmetic
Example 1. Solve X^2 + 1= 2 (mod 7). "Subtract" 1 from both sides the equation becomes
X^2 - 1 = 2 - 1 (mod 7), X^2 = 1 {mod 7} , take square roots of both sides in order to find X.
√x^2 = + or - √ 1 (mod 7), square cancels square root and 'square root' of 1 equals 1
Our solution becomes
X is equals to -1 or + 1 {mod 7}
NOTE: There is no -1 in Modular integers because , only positive and zero integers are applicable in 'Modular operations' . Therefore we add -1 to the mod 7 that is, -1 + 7 {mod 7} = 6 {mod7} .
The solution for x is X = 1 {mod 7} or X = 6 {mod 7}. We have two answers because it is a 'quadratic equation'.
Example two. We are given 2(x - 5) = 2 {mod 8}. Remember, always open the bracket first; simplify . Multiply everything outside the bracket all the things inside the bracket as shown below:
2X - 10 = 2 {mod 8 }. Now collect like terms that is 10 and 2 . The 10 is negative when it crosses over to the 2 it changes to positive, here is what I mean below.
2X = 2 + 10 {mod 8}
Adding ten and two gives 12 , and now we divide the 12 by the coefficient of X that is 2 and our answer is 6mod8 as shown below:
2X = 12 {mod 8}
2X÷2 = 12 ÷ 2 {mod 8}
X = 6 { mod 8}
NOTE: This is how the 'Algebraic modular equations ' are answered. Avoid simplifying before dividing, rather you divide and then follow with 'simplification' if the answer is not an Integer of the given mod.
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