Solve the equation 𝑥 squared plus one equals the square root of three.
When we’re given the instructions “solve the equation,” that means we want to find the value or values for 𝑥 which make the statement true. And to do that, we need to isolate 𝑥 or get 𝑥 by itself. The first thing we can do here is subtract one from both sides of the equation, which will leave us with 𝑥 squared on the left. On the right, we can’t simplify any further. We’ll have the square root of three minus one. Since we have the value of 𝑥 squared, the opposite reciprocal operation will be the square root.
The square root of 𝑥 squared would be 𝑥. But if we take the square root on one side of the equation, we have to take the square root on the other. And this is where we need to be careful. When we’re dealing with an 𝑥 squared term, when we take a square root, we’ll have both a positive and a negative solution. We also need to be careful that we don’t leave out that square root of three inside the square root.
The two values for 𝑥 will be the positive square root of the square root of three minus one and the negative square root of the square root of three minus one.