Question

64х^3-16x^2 + x = 0​

Answer 1

$\displaystyle \tt 64x^3-16x^2+x=0\\\displaystyle \tt x(64x^2-16x+1)=0\\\displaystyle \tt x(8x-1)^2=0\\\displaystyle \tt x_1=0\\\displaystyle \tt 8x-1=0\\\displaystyle \tt 8x=1\\\displaystyle \tt x=\frac{1}{8}\\\displaystyle \tt x_2=0,125$

Answer 2

Ответ:

1/8; 0

Объяснение:

$64 {x}^{3} - 16 {x}^{2} + x = 0 \\ x(64 {x}^{2} - 16x + 1) = 0 \\ x(8x - 1) {}^{2} = 0 \\ x = 0 \\ 8x - 1 = 0 \\ x = \frac{1}{8}$

Answer 3

To solve the given cubic equation, we'll follow the steps to factorize and find the roots. The equation is:

64x^3 - 16x^2 + x = 0

Step 1: Factor out the common term x:

x(64x^2 - 16x + 1) = 0

Step 2: Now, we need to solve the quadratic equation (64x^2 - 16x + 1) = 0. We can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

where a = 64, b = -16, and c = 1.

x = (16 ± √((-16)^2 - 4 * 64 * 1)) / (2 * 64)

x = (16 ± √(256 - 256)) / 128

x = (16 ± √0) / 128

Step 3: Since the discriminant (b^2 - 4ac) is equal to zero, there is only one real root:

x = 16 / 128

x = 1 / 8

So, the real root of the cubic equation is x = 1/8.