Question

Решить уравнение x4-(25x2-60x+36)=0

Answer 1

Решение задания смотри на фотографии

Answer 2

To solve the equation x^4 - (25x^2 - 60x + 36) = 0, we can use factoring. Let's proceed step by step:

Step 1: Factor the quadratic expression inside the parentheses. The quadratic expression inside the parentheses is 25x^2 - 60x + 36. We need to factor this to simplify the equation.

The factors of 25x^2 - 60x + 36 can be found by looking for two numbers that multiply to 25 * 36 = 900 and add up to -60. Those numbers are -30 and -30.

Step 2: Rewrite the equation with the factored expression. x^4 - (25x^2 - 60x + 36) = 0 can be rewritten as: x^4 - (25x^2 - 30x - 30x + 36) = 0

Step 3: Group the terms in pairs and factor by grouping. (x^4 - 25x^2) - (30x - 30x) + 36 = 0

Step 4: Factor out common terms from each group. x^2(x^2 - 25) - 30(x - 1) = 0

Step 5: Factor the difference of squares in the first group. x^2(x - 5)(x + 5) - 30(x - 1) = 0

Step 6: Apply the distributive property to complete factoring. x^2(x - 5)(x + 5) - 30x + 30 = 0

Step 7: Combine like terms. x^2(x - 5)(x + 5) - 30x + 30 = 0

Step 8: Set the equation equal to zero and solve for x. x^2(x - 5)(x + 5) - 30x + 30 = 0

Now, we have a quadratic equation. Let's solve it using any suitable method, such as factoring or the quadratic formula.

x^2(x - 5)(x + 5) - 30x + 30 = 0

The solutions for x can be found by setting each factor equal to zero:

1. x^2 = 0 --> x = 0
2. x - 5 = 0 --> x = 5
3. x + 5 = 0 --> x = -5

So, the solutions to the equation are x = 0, x = 5, and x = -5.