Question

Решить уравнения: (6-х)^2 -(3+x)^2=0

Answer 1

Ответ:

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Answer 2

To solve the equation $(6-x)^2 - (3+x)^2 = 0$, we can use the difference of squares formula, which states that $a^2 - b^2 = (a + b)(a - b)$.

So, let's apply the difference of squares formula to the given equation:

$(6 - x)^2 - (3 + x)^2 = (6 - x + 3 + x)(6 - x - 3 - x) = (9)(3 - 2x) = 0$

Now, we have the equation $9(3 - 2x) = 0$. To solve for $x$, we set each factor to zero:

1. $9 = 0$ (which is not true), or
2. $3 - 2x = 0$

Let's solve for $x$ in the second equation:

$3 - 2x = 0$

Subtract 3 from both sides:

$-2x = -3$

Divide by -2:

$x = \frac{-3}{-2} = \frac{3}{2} = 1.5$

So, the solution to the equation is $x = 1.5$.