Question

1) 2x³-50=0 2) 16x³+8x²+x=0

Answer 1

1)

$2x {}^{3} = 50$

$x {}^{3} = 50$

$x = \sqrt[3]{25}$

2)

$x \times (16x {}^{2} + 8x + 1) = 0$

$x \times (4 + 1) {}^{2} = 0$

$x = 0$

$(4x + 1) {}^{2} = 0$

$x = 0$

$x = - \frac{1}{4}$

Answer 2

$></p> <p><img src=$ или

$16x^2+8x+1=0\\D=64-4*16=0\\x=\frac{-8}{32} =-0,25$

Answer 3

To solve the given equations, we'll find the values of "x" that satisfy each equation. Let's solve them one by one:

1. 2x³ - 50 = 0

Step 1: Bring the constant term to the other side of the equation: 2x³ = 50

Step 2: Divide both sides by 2 to isolate the x³ term: x³ = 50/2 x³ = 25

Step 3: Take the cube root of both sides to find "x": x = ∛(25) x ≈ 2.924

So the solution to the first equation is approximately x = 2.924.

2. 16x³ + 8x² + x = 0

Step 1: Factor out the common term, which is "x": x(16x² + 8x + 1) = 0

Step 2: Now, solve the quadratic equation 16x² + 8x + 1 = 0. You can do this using the quadratic formula or by factoring.

Using the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a

where a = 16, b = 8, and c = 1.

x = (-(8) ± √(8² - 4 * 16 * 1)) / 2 * 16 x = (-8 ± √(64 - 64)) / 32 x = (-8 ± √0) / 32 x = (-8 ± 0) / 32

There are two solutions for x: a) x = (-8 + 0) / 32 x = -8 / 32 x = -1/4

b) x = (-8 - 0) / 32 x = -8 / 32 x = -1/4

So, the solutions to the second equation are x = -1/4 and x = -1/4.

In summary:

1. The solution to 2x³ - 50 = 0 is approximately x = 2.924.
2. The solutions to 16x³ + 8x² + x = 0 are x = -1/4 and x = -1/4 (which means there is a double root at x = -1/4).