(1/(n^2))+(1/n)=(1/(2(n^2)))
multiply through by 2n^2 to get
2 + 2n = 1
n = -1/2
check:
1/(1/4) - 1/(1/2) =? 1/(2/4)
4 - 2 =? 2
yes!
Thank you!
To solve the equation:
(1/(n^2)) + (1/n) = (1/(2(n^2)))
Let's simplify the equation step by step:
Step 1: Find a common denominator for the fractions on the left side.
The common denominator for the fractions is n^2. To get the first fraction's denominator to n^2, we multiply the numerator and denominator by n:
(n/n) * (1/n^2) = (n/n^2)
So, the equation becomes:
(n/n^2) + (1/n) = (1/(2(n^2)))
Step 2: Combine the fractions on the left side of the equation.
(n + n^2) / (n^2) = (1/(2(n^2)))
Step 3: Multiply both sides of the equation by the common denominator.
To get rid of the fractions, we multiply both sides of the equation by 2(n^2):
2(n + n^2) = 1
Step 4: Simplify and rearrange the equation.
2n + 2n^2 = 1
2n^2 + 2n - 1 = 0
Now, we have a quadratic equation in terms of n. To solve it, we can use the quadratic formula:
n = (-b ± √(b^2 - 4ac))/(2a)
In this case, a = 2, b = 2, and c = -1. Plugging these values into the formula, we can find the roots of the equation.