Question

Solve and check: 1/x 3 = x 10/x-2 from least to greatest, the solutions are x = and x =

A. x = -1.68, -1.38
B. x = -1.38, -1.68
C. x = 1.38, 1.68
D. x = 1.68, 1.38

Answer 1

To solve the equation 1/x^3 = x(10/x-2), cross multiply to eliminate the fraction, simplify the equation, factor out an x and solve, and use the quadratic formula to solve for x. The solutions are x=0, x=6.

Step-by-step explanation:

To solve the equation 1/x^3 = x(10/x-2), we need to find the values of x that satisfy the equation. Here's how we can solve it:

1. Cross multiply to eliminate the fraction: (x^3)(10) = 1(x)(x-2)
2. Simplify the equation: 10x^2 - x^2(x-2) = 0
3. Distribute and combine like terms: 10x^2 - x^3 + 2x^2 = 0
4. Arrange the terms in descending order: -x^3 + 12x^2 = 0
5. Factor out an x and solve: x(-x^2 + 12x) = 0
6. Set each factor equal to zero and solve: x = 0 and x^2 - 12x = 0
7. Use the quadratic formula to solve for x in the second equation: x = 0 and x = 12 ± √(144 - 4(1)(0)) / 2
8. Simplify the solutions: x= 0, x = 12 ± √144 / 2

After simplifying, we get x = 0, x = 12 ± 12 / 2, which leads to the solutions x = 0, x = 6.