To find the value of K in the system of equations ك + ب = ٦ and ك × ب = ٨, we can solve for K by substituting the value of ب from the first equation into the second equation.
From the first equation:
ك + ب = ٦
ك = ٦ - ب
Substitute this expression for K into the second equation:
(٦ - ب) × ب = ٨
٦ب - ب² = ٨
ب² - ٦ب + ٨ = ٠
Now, we can solve this quadratic equation using the quadratic formula:
ب = [ ٦ ± √(٦² - 4×١×٨) ] / ٢
ب = [ ٦ ± √(٣٦ - ٣٢) ] / ٢
ب = [ ٦ ± √٤ ] / ٢
ب = [ ٦ ± ٢ ] / ٢
Therefore, ب = ٤ or ب = ٢
Now we can find the corresponding values of K:
ك = ٦ - ب
If ب = ٤:
ك = ٦ - ٤
ك = ٢
If ب = ٢:
ك = ٦ - ٢
ك = ٤
So, the possible values for K are ٢ and ٤.
