Help ?
1. x-3x^1/2+2=0
let u = x^1/2. then you have
u^2 - 3u + 2 = 0
(u-2)(u-1) = 0
u = 1 or 2
so, x^1/2 = 1 or 2
x = 1 or 4
Sure, I can help you with that equation. Let's go step by step to solve it.
1. x - 3x^(1/2) + 2 = 0
To solve this equation, we can use the quadratic formula or the method of factoring.
2. Let's start with the factoring method. We want to rewrite the equation so that we have a squared term. To do this, we can multiply the whole equation by x^(1/2).
x * x^(1/2) - 3x^(1/2) * x^(1/2) + 2 * x^(1/2) = 0 * x^(1/2)
This simplifies to:
x^(3/2) - 3x + 2sqrt(x) = 0
3. Now, we can see that we have a quadratic-like term, x^(3/2), which is convenient for factoring. Let's factor out the common factor of x^(1/2):
x^(1/2) (x - 3) + 2sqrt(x) = 0
4. Now we have (x - 3) as one of the factors. To solve for x, we set each factor equal to zero:
x - 3 = 0
This gives us x = 3 as one solution.
5. The other factor is 2sqrt(x) = 0, which means sqrt(x) = 0. To solve for x, we square both sides:
sqrt(x) = 0
(sqrt(x))^2 = 0^2
x = 0
So, the equation x - 3x^(1/2) + 2 = 0 has two solutions: x = 3 and x = 0.
I hope this explanation was helpful! Let me know if you have any further questions.