Question

2) 5x(x-3)2-5(x-1)3+15(x+2)(x-2)=5;3) (x+2)8-x(3x+1)+(2x+1)(4x2–2x+1)=42.​

Answer 1

2) 10х2-30х-15х+15+15х2-2х+2х-4=5

10х2-30х-15х+15+15-15х2-4=5 находим подобные( с одинаковой буквенной частью)

-5х2-45х+11=5

-5х2=45х-11+5 тут тоже есть подобные

-5х2=45х-6

у=-5х2 парабола точки берем от -3 до 3

у=45х-6 прямая  тут достаточно 2 точек любых

чертить нужно

3) (х+2)³-х(3х+1)²+(2х+1)(4х²-2х+1)=42,

х³+6х²+12х+8-х(9х²+6х+1)+8х³+1=42,

х³+6х²+12х+8-9х³-6х²-х+8х³+1=42,

0+11х+9=42,

11х+9=42,

11х=42-9,

11х=33,

х=3.

Ответ: 3.

Answer 2

Let's solve each of these equations step by step:

2. $5x(x-3)^2 - 5(x-1)^3 + 15(x+2)(x-2) = 5$

First, expand the terms with squared and cubed expressions:

$5x(x^2 - 6x + 9) - 5(x^3 - 3x^2 + 3x - 1) + 15(x^2 - 4) = 5$

Now, distribute the coefficients:

$5x^3 - 30x^2 + 45x - 5x^3 + 15x^2 - 15x + 5x^2 - 20 = 5$

Combine like terms:

$-10x^2 + 45x - 20 = 5$

Now, subtract 5 from both sides:

$-10x^2 + 45x - 20 - 5 = 0$

Simplify further:

$-10x^2 + 45x - 25 = 0$

Now, let's use the quadratic formula to solve for x:

The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.$

In this equation, $a = -10$, $b = 45$, and $c = -25$.

$x = \frac{-45 \pm \sqrt{45^2 - 4(-10)(-25)}}{2(-10)}$

Now, calculate the discriminant (the value inside the square root):

$D = 45^2 - 4(-10)(-25) = 2025 - 1000 = 1025$

Now, plug this value into the quadratic formula:

$x = \frac{-45 \pm \sqrt{1025}}{-20}$

So, the solutions for this equation are:

$x_1 = \frac{-45 + \sqrt{1025}}{-20}$

$x_2 = \frac{-45 - \sqrt{1025}}{-20}$

Now, let's simplify these expressions:

$x_1 = \frac{45 - \sqrt{1025}}{20}$

$x_2 = \frac{45 + \sqrt{1025}}{20}$

3. $(x+2)^8 - x(3x+1) + (2x+1)(4x^2 - 2x + 1) = 42$

First, expand the expressions:

$(x+2)^8 = x^8 + 16x^7 + 112x^6 + 448x^5 + 1120x^4 + 1792x^3 + 1792x^2 + 1024x + 256$

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