Question

(x^2+1)^2-4x^2=(x-1)^2(x+2)^2

Answer 1

Ответ:

$x=\{-1.5;1\}.$

Объяснение:

Раскроем скобки в левой и правой части:

$x^4+2x^2+1-4x^2=(x^2-2x+1)(x^2+4x+4)$

$x^4-2x^2+1=x^4+4x^3+4x^2-2x^3-8x^2-8x+x^2+4x+4$

$2x^3-x^2-4x+3=0$

Полученное уравнение решаем с помощью Microsoft Math Solver

$x=\{-1.5;1\}.$

Answer 2

Let's simplify the given equation step by step:

Starting with the left side of the equation: (x^2 + 1)^2 - 4x^2

Expanding the square: (x^4 + 2x^2 + 1) - 4x^2

Simplifying: x^4 + 2x^2 + 1 - 4x^2

Combining like terms: x^4 - 2x^2 + 1

Now let's simplify the right side of the equation: (x - 1)^2 (x + 2)^2

Expanding each square: (x^2 - 2x + 1) (x^2 + 4x + 4)

Using FOIL (First, Outer, Inner, Last) method to multiply the two binomials: x^2 * x^2 + x^2 * 4x + x^2 * 4 + (-2x) * x^2 + (-2x) * 4x + (-2x) * 4 + 1 * x^2 + 1 * 4x + 1 * 4

Simplifying: x^4 + 4x^3 + 4x^2 - 2x^3 - 8x^2 - 8x + x^2 + 4x + 4

Combining like terms: x^4 + 2x^3 - 3x^2 - 4x + 4

Now we have the simplified equation: x^4 - 2x^2 + 1 = x^4 + 2x^3 - 3x^2 - 4x + 4

We can subtract x^4 from both sides to eliminate the x^4 terms: -2x^2 + 1 = 2x^3 - 3x^2 - 4x + 4

Rearranging the terms: 2x^3 - 3x^2 - 4x + 4 + 2x^2 - 1 = 0

Combining like terms: 2x^3 - x^2 - 4x + 3 = 0

This is the simplified form of the equation (x^2+1)^2-4x^2=(x-1)^2(x+2)^2.