Question

Решите уравнение: 64х^3-16х^2+х=0

Answer 1

To solve the equation 64x^3 - 16x^2 + x = 0, we can use factoring and the zero-product property. Let's break down the process step by step:

Step 1: Factor out the common term In this equation, we can factor out an x: x(64x^2 - 16x + 1) = 0

Step 2: Solve for x by setting each factor equal to zero To find the solutions, we set each factor equal to zero: x = 0 and 64x^2 - 16x + 1 = 0

Step 3: Solve the quadratic equation To solve the quadratic equation 64x^2 - 16x + 1 = 0, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 64, b = -16, and c = 1. Plugging these values into the formula, we get:

x = (-(-16) ± √((-16)^2 - 4(64)(1))) / (2(64)) x = (16 ± √(256 - 256)) / 128 x = (16 ± √0) / 128 x = (16 ± 0) / 128

Step 4: Simplify the solutions Since the discriminant (b^2 - 4ac) is zero, we have a repeated root. The solutions simplify to:

x = 16/128 = 1/8

Therefore, the equation 64x^3 - 16x^2 + x = 0 has one solution: x = 1/8.