Question

(х+1)^2-((1-х^2)/2)=4

Answer 1

(x+1)²-((1-x²)/2)=4

x²+2x+1-(1-x²)/2)=4 |×2

2x²+4x+2-1+x²=8

3x²+4x-7=0      D=100     √D=10

Ответ:  x₁=1       x₂=-7/3.

Answer 2

To solve the equation $(x+1)^2 - \frac{1 - x^2}{2} = 4$, first, let's simplify the equation step by step:

Expand $(x+1)^2$: $x^2 + 2x + 1 - \frac{1 - x^2}{2} = 4$

Now, simplify the equation further: $x^2 + 2x + 1 - \frac{1}{2} + \frac{x^2}{2} = 4$

Combine like terms: $\frac{3x^2}{2} + 2x - \frac{1}{2} = 4 - 1$

$3x^2 + 4x - 1 = 7$

Now, move all the terms to one side to set the equation to zero: $3x^2 + 4x - 8 = 0$

Now, you can solve this quadratic equation by factoring, completing the square, or by using the quadratic formula. In this case, using the quadratic formula might be the most straightforward approach:

The quadratic formula states that for an equation in the form $ax^2 + bx + c = 0$, the solutions for $x$ are given by:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

In your equation, $a = 3$, $b = 4$, and $c = -8$. Plugging these values into the formula, the solutions for $x$ can be calculated. Note that you will get two solutions due to the ± sign in the formula.