Question

Решить уравнение Корень из (x^2 + x -3) = Корень из (1-2x)

Answer 1

$\sqrt{x^2+x-3}= \sqrt{1-2x}$
$x^2+x-3=1-2x$
$x^{2} +3x-4=0$
$(x-1)(x+4)=0$
$x_1=1$
$x_2=-4$

Answer 2

I can help you with your math problem. Here is the solution:

To solve the equation $\sqrt{x^2+x-3}=\sqrt{1-2x}$, we need to follow these steps:

- Square both sides of the equation to get rid of the square roots: $x^2+x-3=1-2x$. - Simplify and rearrange the equation to get a quadratic form: $x^2+3x-4=0$. - Factor the quadratic expression using the method of your choice. For example, we can use the AC method: $x^2+3x-4=(x+4)(x-1)=0$. - Set each factor equal to zero and solve for x: $x+4=0$ or $x-1=0$. Therefore, $x=-4$ or $x=1$. - Check the solutions by plugging them back into the original equation. We find that $x=-4$ is an extraneous solution, since it makes the left side of the equation negative, which is not possible for a square root. Therefore, the only valid solution is $x=1$.Ответь+подробно.+Решить+уравнение+Корень+из+(x^2+++x+-3)+=+Корень+из+(1-2x)