Question

(x^-1)(x^+3)=(x^+1)+ xрешить

Answer 1

Ответ:

х= -4

Объяснение:

(x²-1)(x²+3)=(x²+1)²+x

х⁴+3х²-х²-3=х⁴+2х+1+х

х⁴+2х²-х⁴-2х²-х=1+3

-х=4

х= -4

Answer 2

To solve the equation (x^-1)(x^+3) = (x^+1) + x, let's follow these steps:

Step 1: Simplify the left-hand side (LHS) of the equation. Step 2: Expand the right-hand side (RHS) of the equation. Step 3: Combine like terms. Step 4: Move all the x terms to one side of the equation. Step 5: Factor out x from the resulting equation. Step 6: Solve for x.

Let's get started:

Step 1: Simplify the LHS: (x^-1)(x^+3) = (1/x)(x+3) = (x+3)/x

Step 2: Expand the RHS: (x^+1) + x = x + 1 + x = 2x + 1

Step 3: Combine like terms: (x+3)/x = 2x + 1

Step 4: Move all the x terms to one side: (x+3)/x - 2x = 1

Step 5: Factor out x: [(x+3) - 2x^2] / x = 1

Step 6: Solve for x: Multiply both sides by x to eliminate the fraction: (x + 3) - 2x^2 = x

Now, let's move all terms to one side and set the equation to zero: 2x^2 + x - (x + 3) = 0

Simplify: 2x^2 + x - x - 3 = 0 2x^2 - 3 = 0

Now, we have a quadratic equation in the form of ax^2 + bx + c = 0, where a = 2, b = 0, and c = -3. To solve this quadratic equation, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

Substitute the values: x = (0 ± √(0^2 - 42(-3))) / 2*2 x = (±√(24)) / 4

Now, we have two potential solutions for x:

1. x = (√24) / 4 ≈ 0.866
2. x = -(√24) / 4 ≈ -0.866

So, the solutions for the equation are approximately x ≈ 0.866 and x ≈ -0.866.