Which are the solutions of 18x^3=50x?
A. 0,5/3
B. -5/3,5/3
C. -5/3,0,5/3
D. -5/3,1,5/3
I don't know how to get the answer.
18x^3 - 50x = 0
x(18x^2 - 50) = 0
x = 0 or x^2 = 50/18 = 25/9
so x=0 or x= ±5/3
I don't understand how you get x^2=50/18
from
x(18x^2 - 50) = 0
x = 0 or 18x^2 - 50 = 0
18x^2 = 50 now divide both sides by 18
x^2 = 50/18 which reduces to 25/9
x^2 = 25/9
From there I got my final answer by taking the square root of both sides
To find the solutions of the equation 18x^3 = 50x, we can follow these steps:
Step 1: Start by setting the equation equal to 0 by subtracting 50x from both sides:
18x^3 - 50x = 0
Step 2: Factor out the common term:
x(18x^2 - 50) = 0
Step 3: Apply the zero product property, which states that if a product is equal to zero, then at least one of the factors must be zero. So, we have two cases to consider:
Case 1: x = 0
If x = 0, then the left-hand side becomes 0(18(0)^2 - 50) = 0. Therefore, x = 0 is one solution.
Case 2: 18x^2 - 50 = 0
To solve this quadratic equation, we can factor or use the quadratic formula.
Factoring method:
Start by factoring out the greatest common factor:
2(9x^2 - 25) = 0
Now, we have a difference of squares:
2(3x - 5)(3x + 5) = 0
Using the zero product property again:
2(3x - 5) = 0 or 2(3x + 5) = 0
Solving these two equations:
3x - 5 = 0 or 3x + 5 = 0
Solutions for case 2:
From the first equation, add 5 to both sides and divide by 3:
3x = 5
x = 5/3
From the second equation, subtract 5 from both sides and divide by 3:
3x = -5
x = -5/3
So, the solutions for case 2 are x = 5/3 and x = -5/3.
Therefore, the solutions of the given equation are:
x = 0, x = 5/3, and x = -5/3.
Looking at the answer choices provided:
A. 0, 5/3
B. -5/3, 5/3
C. -5/3, 0, 5/3
D. -5/3, 1, 5/3
The correct answer is C. -5/3, 0, 5/3.