For what positive integer n is 2n+3n+4n=nn?
divide both sides by n
2+3+4=n
To find the value of n for which the equation 2n + 3n + 4n = nn is true, we need to simplify the equation and solve for n.
First, let's simplify the left side of the equation by combining like terms:
2n + 3n + 4n = nn
(2 + 3 + 4) n = nn
9n = nn
Now, we can solve this equation by considering different cases:
Case 1: n = 0
Substituting n = 0 into the equation, we get:
9(0) = (0)(0)
0 = 0
Since this is true, n = 0 is a solution.
Case 2: n ≠ 0
In this case, we can divide both sides of the equation by n:
9 = n
So, for n ≠ 0, the solution is n = 9.
Therefore, the positive integer value of n that satisfies the equation 2n + 3n + 4n = nn is n = 9.
To find the positive integer value of n that satisfies the equation 2n + 3n + 4n = nn, we can start by simplifying the equation on the left-hand side:
2n + 3n + 4n = nn
Adding like terms, we get:
9n = nn
Next, we can rearrange the equation to isolate n on one side:
nn - 9n = 0
Factoring out n, we have:
n(n - 9) = 0
This equation can be satisfied if either n = 0 or n - 9 = 0. However, we are looking for positive integer values of n, so we can only consider n - 9 = 0.
Solving n - 9 = 0, we find:
n = 9
Therefore, the positive integer value of n that satisfies the equation 2n + 3n + 4n = nn is n = 9.