Question

1. x^3-x^2=0 2. x^6-4x^3+4=0 3. x^2-25=0

Answer 1

1) x^2(x-1)=0
x=0
x=1
2)x^3=t
t^2-4t+4=0
(t-2)^2=0
x^3-2=0
x=корень 3 степени из 2
3)x^2=25
x=+-5

Answer 2

1. x³-x²=0  
x²(x-1)=0 
x²= 0 или x-1=0 
x₁=0
x₂=1 
2. x⁶-4x³+4=0
(x³-2)²=0 
x³-2=0
x³=2 
x=³√2 
3. x²-25=0
x²=25 
x₁=5 
x₂=-5 

Answer 3

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

1. x^3 - x^2 = 0: Factor out x^2 from both terms: x^2(x - 1) = 0

   Now, set each factor equal to zero and solve for x: x^2 = 0 x = 0

   x - 1 = 0 x = 1

   So, the solutions are x = 0 and x = 1.

2. x^6 - 4x^3 + 4 = 0: This equation can be rewritten as a quadratic equation in terms of x^3: (x^3)^2 - 4x^3 + 4 = 0

   Let y = x^3: y^2 - 4y + 4 = 0

   This is a quadratic equation in y, and we can factor it: (y - 2)^2 = 0

   Take the square root of both sides: y - 2 = 0 y = 2

   Now, revert back to x^3: x^3 = 2

   To solve for x, take the cube root of both sides: x = ∛2

   So, the solution is x = ∛2.

3. x^2 - 25 = 0: This is a simple quadratic equation. To solve it, factor or use the quadratic formula: x^2 - 25 = 0 (x - 5)(x + 5) = 0

   Set each factor equal to zero and solve for x: x - 5 = 0 x = 5

   x + 5 = 0 x = -5

   So, the solutions are x = 5 and x = -5.