Question

(x-3)^4-3 (x-3)^2-10=0 напишите полное решение уравнения

Answer 1

(х-3)²=а: 
а²-3а-10=0:
(а-5)((а+2)=0: а1=5:а2=-2:
(х-3)²=5: х²-6х+9-5=0: х²-6х+4=0:
х1=(6-2√5)/2: х2=(6+2√5)/2:
(х-3)²=-2: х²-6х+9+2=0: х²-6х+11=0:
Д=36-44=-8: не имеет значение

 

Answer 2

(x-3)^2=y, получается квадратное уравнение: 
y^2-3y-10=0,
D=9-4*(-10)=49=7^2
y1=3-7/2=-4/2=-1, y2=3+7/2=5. Ищем теперь корни x,подставляя получившиеся корни y в уравнение (x-3)^2=y.
(x-3)^2=-1
x^2-6x+9+1=0
D=36-4*10=-4, корней нет.
(x-3)^2=5.
x^2-6x+9-5=0
x^2-6x+4=0
D=36-4*4=20
x1=6- корень из 20/2=3- корень из 20
x2=3+корень из 20.

Answer 3

Solving the Equation:

To solve the equation (x-3)^4 - 3 + (x-3)^2 - 10 = 0, we can use the substitution method to simplify the equation and then solve for the value of x.

First, let's simplify the equation by substituting (x-3)^2 as y.

So, the equation becomes: y^2 - 3 + y - 10 = 0.

Now, we can solve for y and then find the corresponding values of x.

Solving for y:

To solve for y, we can treat the equation y^2 - 3 + y - 10 = 0 as a quadratic equation in terms of y.

The equation becomes: y^2 + y - 13 = 0.

Using the quadratic formula: y = (-b ± √(b^2 - 4ac)) / (2a), where a = 1, b = 1, and c = -13.

The solutions for y are: y = (-1 + √(1^2 - 4*1*(-13))) / (2*1) = (-1 + √(1 + 52)) / 2 = (-1 + √53) / 2 and y = (-1 - √(1^2 - 4*1*(-13))) / (2*1) = (-1 - √(1 + 52)) / 2 = (-1 - √53) / 2.

Finding the Corresponding Values of x:

Now that we have the values of y, we can substitute back to find the corresponding values of x.

For y = (-1 + √53) / 2: (x-3)^2 = (-1 + √53) / 2.

For y = (-1 - √53) / 2: (x-3)^2 = (-1 - √53) / 2.

Taking the square root of both sides, we get: x - 3 = ±√((-1 + √53) / 2) and x - 3 = ±√((-1 - √53) / 2).

Finally, solving for x, we have: x = 3 ± √((-1 + √53) / 2) and x = 3 ± √((-1 - √53) / 2).

So, the solutions for the equation (x-3)^4 - 3 + (x-3)^2 - 10 = 0 are: x = 3 + √((-1 + √53) / 2), x = 3 - √((-1 + √53) / 2), x = 3 + √((-1 - √53) / 2), and x = 3 - √((-1 - √53) / 2).

This is the complete solution to the given equation.