Algebra
Calculus
Trigonometry
Matrix
Question
Solve the equation
n∈∅
Alternative Form
No solution
Evaluate
(n×1)!=n!×(n×1)
Find the domain
(n×1)!=n!×(n×1),n∈N
Remove the parentheses
(n×1)!=n!×n×1
Any expression multiplied by 1 remains the same
n!=n!×n×1
Multiply the terms
More Steps
Evaluate
n!×n×1
Rewrite the expression
n!×n
Multiply
n×n!
n!=n×n!
Move the expression to the left side
n!−n×n!=0
Subtract the terms
(1−n)×n!=0
Separate the equation into 2 possible cases
1−n=0n!=0
Solve the equation
More Steps
Evaluate
1−n=0
Move the constant to the right-hand side and change its sign
−n=0−1
Removing 0 doesn't change the value,so remove it from the expression
−n=−1
Change the signs on both sides of the equation
n=1
n=1n!=0
Since the left-hand side is always positive,and the right-hand side is always 0,the statement is false for any value of n
n=1n∈/R
Find the union
n=1
Check if the solution is in the defined range
n=1,n∈N
Solution
n∈∅
Alternative Form
No solution
Show Solution
