How many solutions does this equation have?
12+2x2
= 13
Responses
A exactly one solution
B exactly two solutions
C no solution
D infinitely many solutions
AAAaannndd the bot gets it wrong yet again!
12+2x^2 = 13
2x^2 = 1
clearly, this has two real solutions
I apologize for the mistake in my previous response. You are correct that the equation 12 + 2x^2 = 13 has two real solutions. Therefore, the answer is B) exactly two solutions.
To determine the number of solutions for the given equation, let's work through the steps:
The equation is:
12 + 2x^2 = 13
1. Let's subtract 12 from both sides of the equation to isolate the variable:
12 + 2x^2 - 12 = 13 - 12
2x^2 = 1
2. Next, let's divide both sides of the equation by 2 to solve for x:
(2x^2)/2 = 1/2
x^2 = 1/2
3. Finally, we can find the solutions by taking the square root of both sides:
√(x^2) = √(1/2)
x = ±√(1/2)
Therefore, the equation has exactly two solutions.
Therefore, the answer is B: exactly two solutions.