Question

(x^2+3x-4)^3+(2x^2-5x+3)^3=(3x^2-2x-1)^3

Answer 1

!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer 2

Вот тебе ответ я на пк сделал разберись

Answer 3

Let's expand each side of the given equation and see if they are equal. First, let's expand each cube:

1. Expanding (x^2 + 3x - 4)^3: (x^2 + 3x - 4)^3 = (x^2 + 3x - 4)(x^2 + 3x - 4)(x^2 + 3x - 4)

Using the binomial expansion formula, we get: (x^2 + 3x - 4)^3 = (x^2)^3 + 3(x^2)^2(3x) + 3(x^2)(3x)^2 + (3x)^3 - 4[(x^2)^2 + 3(x^2)(3x) + 3(x^2)(3x) + (3x)^2] + 16(x^2 + 3x - 4)

Simplifying further: (x^2 + 3x - 4)^3 = x^6 + 9x^4 + 27x^3 + 27x^2 - 48x^2 - 36x^2 + 108x - 108x + 64x^2 - 192x + 64

Combining like terms: (x^2 + 3x - 4)^3 = x^6 + 9x^4 - 57x^2 - 84x + 64

2. Expanding (2x^2 - 5x + 3)^3: (2x^2 - 5x + 3)^3 = (2x^2 - 5x + 3)(2x^2 - 5x + 3)(2x^2 - 5x + 3)

Using the binomial expansion formula, we get: (2x^2 - 5x + 3)^3 = (2x^2)^3 + 3(2x^2)^2(-5x) + 3(2x^2)(-5x)^2 + (-5x)^3 + 3[(2x^2)^2(3) + (2x^2)(-5x)(3) + (2x^2)(3)(-5x) + (-5x)^2(3)] + 9(2x^2)(-5x) + 27(2x^2) - 45x^2 + 27(3x) - 81x + 27

Simplifying further: (2x^2 - 5x + 3)^3 = 8x^6 - 60x^4 + 150x^3 - 125x^3 + 450x^2 - 270x^2 - 675x^2 + 405x - 405x + 27

Combining like terms: (2x^2 - 5x + 3)^3 = 8x^6 - 60x^4 + 25x^3 + 360x^2 - 810x + 27

3. Expanding (3x^2 - 2x - 1)^3: (3x^2 - 2x - 1)^3 = (3x^2 - 2x - 1)(3x^2 - 2x - 1)(3x^2 - 2x - 1)

Using the binomial expansion formula, we get: (3x^2 - 2x - 1)^3 = (3x^2)^3 + 3(3x^2)^2(-2x) + 3(3x^2)(-2x)^2 + (-2x)^3 - 2[(3x^2)^2 + 3(3x^2)(-2x) + 3(3x^2)(-2x) + (-2x)^2] - 6(3x^2)(-2x) - 18(3x^2) + 12x^2 - 12x + 1

Simplifying further: (3x^2 - 2x - 1)^3 = 27x^6 - 54x^4 + 36x^2 - 8x^3 - 18x^2 + 4x^2 + 12x^2 - 12x + 1

Combining like terms: (3x^2 - 2x - 1)^3 = 27x^6 - 8x^3 - 20x^2 - 12x + 1

Now let's check if the original equation holds:

(x^2 + 3x - 4)^3 + (2x^2 - 5x + 3)^3 = (3x^2 - 2x - 1)^3

Substitute the expanded forms: (x^6 + 9x^4 - 57x^2 - 84x + 64) + (8x^6 - 60x^4 + 25x^3 + 360x^2 - 810x + 27) = 27x^6 - 8x^3 - 20x^2 - 12x + 1

Combine like terms on the left side: 9x^6 - 51x^4 + 25x^3 + 303x^2 - 894x + 91 = 27x^6 - 8x^3 - 20x^2 - 12x + 1

Now, move all terms to one side to check for equality: 9x^6 - 27x^6 - 51x^4 + 25x^3 + 303x^2 + 20x^2 - 8x^3 + 12x - 894x + 91 - 1 = 0

Simplify further: -18x^6 - 51x^4 + 17x^3 + 323x^2 - 882x + 90 = 0

The equation is not balanced, so the initial statement is incorrect:

(x^2 + 3x - 4)^3 + (2x^2 - 5x + 3)^3 ≠ (3x^2 - 2x - 1)^3