- #1
Dil1
- 2
- 0
solve the equation
3x^(-1/2) - 4 = 0
3x^(-1/2) - 4 = 0
MarkFL said:I've moved this thread here to our algebra forum since this is a better fit given the question.
We are given to solve:
\(\displaystyle 3x^{-\frac{1}{2}}-4=0\)
What do we get if we multiply through by $x^{\frac{1}{2}}\ne0$?
Dil said:i don't get it?
The equation 3x^(-1/2) - 4 = 0 is a mathematical expression that represents a relationship between two quantities, x and y. In this equation, x is raised to the power of -1/2, or 1 divided by the square root of x, and is equal to 4 divided by 3. This means that when x is multiplied by itself, then raised to the power of -1/2, the result will be 4 divided by 3.
To solve this equation, you can use algebraic methods to isolate the variable x. First, add 4 to both sides of the equation to get 3x^(-1/2) = 4. Then, multiply both sides by the reciprocal of 3, which is 1/3, to get x^(-1/2) = 4/3. Next, raise both sides of the equation to the power of -2 to get x = (4/3)^(-2). Finally, simplify the right side of the equation to get x = 9/16. Therefore, the solution to the equation is x = 9/16.
No, this equation can only have one solution because there is only one value of x that will make the equation true. When solving equations with variables in the exponent, it is important to check the solutions to make sure they are valid. In this case, x = 9/16 is the only solution that works for the given equation.
The domain of this equation is all real numbers except 0, since you cannot divide by 0. The range, or the set of all possible output values, is all real numbers greater than or equal to 0. This is because the power of -1/2 means that the output will be the reciprocal of the square root of the input, and the square root of a number can never be negative.
This equation can be used to solve problems involving rates, such as conversions between units or calculating the time it takes for an object to travel a certain distance. For example, if x represents the speed of an object in meters per second, then 3x^(-1/2) - 4 = 0 could represent the time it takes for the object to travel 4 meters. By solving for x, you could determine the speed needed for the object to reach that distance in a certain amount of time.