Question

Решите уравнение x^4+7x^2-18=0

Answer 1

Решение на фотографии.

Answer 2

To solve the equation x^4 + 7x^2 - 18 = 0, we can use a substitution to simplify it. Let's make a substitution: Let y = x^2.

Now, the equation becomes a quadratic equation in terms of y:

y^2 + 7y - 18 = 0

To solve this quadratic equation, we can factor it:

(y + 9)(y - 2) = 0

Now, set each factor to zero and solve for y:

1. y + 9 = 0 => y = -9
2. y - 2 = 0 => y = 2

Now, revert the substitution by setting y back to x^2:

1. x^2 = -9 Taking the square root of both sides (remembering both positive and negative roots):

x = ±√(-9) => x = ±3i (where 'i' is the imaginary unit, √(-1))

2. x^2 = 2 Taking the square root of both sides:

x = ±√2

So, the solutions to the original equation are: x = √2, -√2, 3i, -3i.