Question

(5х+4)^2(x-2)=(5x-4)(x-2)^2

Answer 1

Ответ:

2, (-27 - √569)/20, (-27 + √569)/20

Пошаговое объяснение:

(5x+4)²(x-2) - (5x-4)(x-2)² = 0

(x-2)(25x² + 40x + 16 - 5x² + 4x + 10x - 8) = 0

(x-2)(20x² + 54x + 8) = 0

x1 = 2

20x² + 54x + 8 = 0

10x² + 27x + 4 = 0

D = 729 - 160 = 569

x2 = (-27 - √569)/20

x3 = (-27 + √569)/20

Answer 2

Let's solve the given equation step by step:

(5x + 4)^2(x - 2) = (5x - 4)(x - 2)^2

First, expand both sides of the equation:

(25x^2 + 40x + 16)(x - 2) = (5x - 4)(x^2 - 4x + 4)

Now, simplify and distribute on both sides:

25x^3 - 50x^2 + 40x^2 - 80x + 16x - 32 = 5x^3 - 20x^2 + 20x - 4x^2 + 16x - 16

Combine like terms:

25x^3 - 10x^2 - 24x - 32 = 5x^3 - 4x^2 + 36x - 16

Next, move all terms to one side to set the equation to zero:

25x^3 - 5x^3 - 10x^2 + 4x^2 - 24x - 36x - 32 + 16 = 0

Combine like terms again:

20x^3 - 6x^2 - 60x - 16 = 0

Now, we have a cubic equation. Unfortunately, cubic equations do not have a general formula for solving them like quadratic equations do. We'll need to solve it using numerical methods or approximations.

One common method is to use numerical solvers or graphing calculators to find approximate solutions. Another method is to apply iterative numerical techniques such as the Newton-Raphson method or the bisection method.

Keep in mind that finding the exact solutions may not be possible or practical in this case.