Question
Question: How do you solve \[2{n^2} = - 144?\]...
How do you solve 2n2=−144?
Solution
Hint : In order to solve this question, we have to follow certain steps and find the value of the variable n. The given equation contains a negative value on the right side of the equation and a square on the variable n therefore we use the definition of ‘i’ to solve this problem.
Complete step-by-step answer :
Given to us is an equation 2n2=−144
We have to now find the value of the variable n.
In order to do this, let us first divide both the sides of the equation by 2
So now we can write this equation as 22n2=−2144
We can solve this equation to get n2=−72
In order to find the value of the variable n, let us now take square root on both sides of the equation.
The equation now becomes
n2=−72
The square and root on the left side of the equation get cancelled to give
n=−72
Here, we see that there is a negative value inside the square root. We know that a negative value inside a square root is an imaginary value. We can write this as follows.
n=−1×72
This can also be written as
n=−1×72
Now, we know that −1=i , by substituting this in the above equation, we get
n=i72
We can also write this as
n=i36×2
On solving this we get
n=±6i2
Hence we solve the given equation to get the final value as n=±6i2
So, the correct answer is “ n=±6i2 ”.
Note : It is to be noted that any negative value inside a square root does not exist so it is an imaginary value. This imaginary value is denoted as i where i=−1 . This value denotes that the number is imaginary.