Solve:
2x-9√x +4=0
change sqrt x = u
2u^2-9u+4=0
(2u-1)(u-4)=0
solve for u, then x=u^2
1/4,16
Thanks for the help.
To solve the equation 2x - 9√x + 4 = 0, we can approach it by using a technique called substitution. Let's get started:
Step 1: Let's substitute a new variable to make the equation more manageable. Let's assume y = √x.
Step 2: Using the substitution, we can rewrite the equation as 2y^2 - 9y + 4 = 0. Now we have a quadratic equation in terms of y.
Step 3: Factor the quadratic equation. In this case, the equation can be factored as (2y - 1)(y - 4) = 0.
Step 4: Set each factor equal to zero and solve for y:
- Setting 2y - 1 = 0, we get y = 1/2.
- Setting y - 4 = 0, we get y = 4.
Step 5: Now, substitute back y = √x into the equation to find the values of x:
- When y = 1/2, √x = 1/2. Squaring both sides, we get x = 1/4.
- When y = 4, √x = 4. Squaring both sides, we get x = 16.
So, the solutions to the equation 2x - 9√x + 4 = 0 are x = 1/4 and x = 16.