can someone check me and see if this is correct.
�ã(4x+1) + 3 = 0
�ã(4x+1)= -3
�ã(4x+1).2= -3.2
4x + 1 = 9
4x = 9 - 1
4x = 8
x = -2
not sure what your symbol ã means but it appears like you mean square root.
If that is the case then in your second line
√(4x+1)= -3 you could stop, since by definition the square root symbol says to take the positive square root of a number.
So it could not be a negative.
Your solution would be:
No solution in the real number set
It seems like there might be a mistake in the calculation. Let's go through the steps to solve the equation and find the correct answer:
�ã(4x+1) + 3 = 0
�ã(4x+1) = -3
Taking the square root of both sides, we get:
4x+1 = -√3
Now, subtracting 1 from both sides, we have:
4x = -√3 - 1
Since we know that the square root of a number is always positive, there is no need to consider the negative square root of 3 in our calculation. Therefore, the equation is unsolvable in the real number set, which means there is no real solution for x.
Therefore, the correct answer is:
No solution in the real number set
You are correct in your interpretation of the symbol ã as the square root symbol (√). However, there seems to be a mistake in your calculations.
Starting with the given equation:
√(4x+1) + 3 = 0
Subtracting 3 from both sides:
√(4x+1) = -3
Here is where the mistake occurs. The square root of a number is always non-negative, so it cannot be equal to a negative value. Therefore, there are no solutions for x in the given equation.
The correct conclusion would be:
No solutions in the real number set.