Question

Solve the equation x⁹ = x¹0x⁹ = x² 20x 100x² 81 = x² 100x² 81 = x² 20x 100 for x.

a) 1
b) 3
c) 5
d) 9

Answer 1

To solve the equation x⁹ = x¹0x⁹ = x² 20x 100x² 81 = x² 100x² 81 = x² 20x 100 for x, we can simplify the equation by combining like terms and then use the quadratic formula to find the solution. However, after solving the quadratic equation, we find that there is no real solution for x.

Step-by-step explanation:

To solve the equation x⁹ = x¹0x⁹ = x² 20x 100x² 81 = x² 100x² 81 = x² 20x 100 for x, we can simplify the equation by combining like terms. Here's the step-by-step solution:

1. Combine like terms: x² + 20x + 100 = x² + 100x² + 81 = x² + 20x + 100
2. Subtract x² and 20x from both sides: 100 = 100x² + 81
3. Subtract 100 from both sides: 0 = 100x² - 19

Now, we have a quadratic equation. Since the equation is not factorable, we can solve it using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a)

For the equation 100x² - 19 = 0, a = 100, b = 0, and c = -19. Plugging these values into the quadratic formula, we get:

x = (-0 ± √(0² - 4(100)(-19))) / (2(100))

After simplifying the equation, we find that the roots are imaginary. Therefore, there is no real solution for x in this equation.