Question

X^4 -8x^3-4x^2+16x+4=0

Answer 1

X³-4x²-16x+64=0
х²(х-4)-16(х-4)=0
(х-4)(х²-16)=0
(х-4)(х-4)(х+4)=0
х-4=0 или х+4=0
х=4 х=-4
Ответ :-4 и 4

Answer 2

To solve the equation X^4 - 8x^3 - 4x^2 + 16x + 4 = 0, you can use various methods such as factoring, synthetic division, or numerical methods. However, in this case, it's not easily factorable, so we'll resort to numerical methods.

One popular numerical method to approximate the roots of an equation is the Newton-Raphson method. To apply this method, we'll need an initial guess for the root and iterate to refine the approximation until we get an accurate result.

Let's use an initial guess of x = 1:

1st iteration: f(x) = x^4 - 8x^3 - 4x^2 + 16x + 4 f'(x) = 4x^3 - 24x^2 - 8x + 16

Using the Newton-Raphson formula: x1 = x0 - f(x0)/f'(x0)

x1 = 1 - (1^4 - 8(1)^3 - 4(1)^2 + 16(1) + 4)/(4(1)^3 - 24(1)^2 - 8(1) + 16) x1 = 1 - (-1)/(4 - 24 - 8 + 16) x1 = 1 - (-1)/(-12) x1 = 1 + 1/12 x1 = 13/12

2nd iteration: x2 = x1 - f(x1)/f'(x1)

Repeat the above steps until you reach an accurate solution. It may take a few iterations to converge to a root. Alternatively, you can use numerical software or calculators to find the roots of the equation more precisely.