Question

(х²-6х²)+(х²-6х)-56=0

Answer 1

Вероятно уравнение должно быть записано так :
(x² - 6x)² + (x² - 6x) - 56 = 0
Если так, то решается оно таким образом:
Сделаем замену:
x² - 6x = m
m² + m - 56 = 0
D = 1² - 4 * 1 * (- 56) = 1 + 224 = 225 = 15²
$m_{1} = \frac{-1+15}{2}=7\\\\ m_{2} = \frac{-1-15}{2}=-8$
Вернёмся к замене:
$x^{2} -6x=7\\\\ x^{2} -6x-7=0\\\\D=(-6) ^{2} -4*1*(-7)=36 + 28=64= 8^{2}\\\\ x_{1} = \frac{6+8}{2}=7\\\\ x_{2}= \frac{6-8}{2}=-1\\\\\\ x^{2} -6x=-8\\\\ x^{2} -6x+8=0\\\\D=(-6) ^{2}-4*1*8=36-32=4= 2^{2} \\\\ x_{3}= \frac{6+2}{2}=4\\\\ x_{4}= \frac{6-2}{2} =2$
Ответ: - 1 ; 2 ; 4 ; 7

Answer 2

It looks like there might be a typographical error in your equation. I assume you meant to write:

x² - 6x + (x² - 6x) - 56 = 0

To solve this quadratic equation, let's first combine the like terms:

2x² - 12x - 56 = 0

Now, we have a quadratic equation in the standard form of ax² + bx + c = 0, where a = 2, b = -12, and c = -56.

To solve for x, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

Plugging in the values, we get:

x = (12 ± √((-12)² - 4 * 2 * (-56))) / (2 * 2)

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

Discriminant (D) = b² - 4ac D = (-12)² - 4 * 2 * (-56) = 144 + 448 = 592

Since the discriminant (D) is positive, we have two real solutions:

x = (12 + √592) / 4 x = (12 - √592) / 4

Now, let's approximate these values:

x ≈ (12 + √592) / 4 ≈ (12 + 24.33) / 4 ≈ 36.33 / 4 ≈ 9.08

x ≈ (12 - √592) / 4 ≈ (12 - 24.33) / 4 ≈ -12.33 / 4 ≈ -3.08

So, the two solutions to the equation are approximately x ≈ 9.08 and x ≈ -3.08.