Question

(x+5x)²-4(x²+5x)-12=0 (x²+4x)²-3(x²+4x)=10 (x²-4x)²-2(x²-4x)-15=0

Answer 1

Ответ:

$25 \times 2$

Answer 2

Let's solve each quadratic equation step by step:

1. (x+5x)² - 4(x²+5x) - 12 = 0

First, simplify the equation: (6x)² - 4(x² + 5x) - 12 = 0 36x² - 4x² - 20x - 12 = 0 32x² - 20x - 12 = 0

Now, we can factor this quadratic equation: 4(8x² - 5x - 3) = 0

Now, set each factor to zero and solve for x: 8x² - 5x - 3 = 0 Using the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a

In this case, a = 8, b = -5, and c = -3. x = (5 ± √((-5)² - 4 * 8 * (-3))) / 2 * 8 x = (5 ± √(25 + 96)) / 16 x = (5 ± √121) / 16 x = (5 ± 11) / 16

So, the solutions are: x = (5 + 11) / 16 = 16 / 16 = 1 x = (5 - 11) / 16 = -6 / 16 = -3/4

2. (x² + 4x)² - 3(x² + 4x) = 10

Let's simplify the equation: (x² + 4x)² - 3(x² + 4x) - 10 = 0

Now, let's make a substitution: Let y = (x² + 4x) Now the equation becomes: y² - 3y - 10 = 0

Factor the quadratic equation: (y - 5)(y + 2) = 0

Now set each factor to zero and solve for y: y - 5 = 0 --> y = 5 y + 2 = 0 --> y = -2

Now, substitute back y = (x² + 4x): x² + 4x = 5 --> x² + 4x - 5 = 0

Now factor the quadratic equation: (x + 5)(x - 1) = 0

Set each factor to zero and solve for x: x + 5 = 0 --> x = -5 x - 1 = 0 --> x = 1

So, the solutions are: x = -5 and x = 1

3. (x² - 4x)² - 2(x² - 4x) - 15 = 0

Let's simplify the equation: (x² - 4x)² - 2(x² - 4x) - 15 = 0

Now, let's make a substitution: Let y = (x² - 4x) Now the equation becomes: y² - 2y - 15 = 0

Factor the quadratic equation: (y - 5)(y + 3) = 0

Now set each factor to zero and solve for y: y - 5 = 0 --> y = 5 y + 3 = 0 --> y = -3

Now, substitute back y = (x² - 4x): x² - 4x = 5 --> x² - 4x - 5 = 0

Now factor the quadratic equation: (x + 1)(x - 5) = 0

Set each factor to zero and solve for x: x + 1 = 0 --> x = -1 x - 5 = 0 --> x = 5

So, the solutions are: x = -1 and x = 5

To summarize:

1. The solutions to the first equation are x = 1 and x = -3/4.
2. The solutions to the second equation are x = -5 and x = 1.
3. The solutions to the third equation are x = -1 and x = 5.