Question

Корень 5 = корень х^2 -4 помогите срочноо

Answer 1

Возводишь обе части уравнения в квадрат:
5=X^2-4
X^2=5-4=1
X=+/-1

Answer 2

Solving the Equation: $\sqrt{5} = \sqrt{x^2 - 4}$

To solve the equation $\sqrt{5} = \sqrt{x^2 - 4}$, we need to isolate the variable $x$.

First, we square both sides of the equation to eliminate the square roots:

$(\sqrt{5})^2 = (\sqrt{x^2 - 4})^2$

Simplifying, we get:

$5 = x^2 - 4$

Next, we add 4 to both sides of the equation:

$5 + 4 = x^2 - 4 + 4$

Simplifying further, we have:

$9 = x^2$

To solve for $x$, we take the square root of both sides of the equation:

$\sqrt{9} = \sqrt{x^2}$

This gives us:

$3 = x$

Therefore, the solution to the equation $\sqrt{5} = \sqrt{x^2 - 4}$ is $x = 3$.

Note: It's important to verify the solution by substituting it back into the original equation to ensure it satisfies the equation. In this case, substituting $x = 3$ into the equation $\sqrt{5} = \sqrt{x^2 - 4}$ gives us $\sqrt{5} = \sqrt{3^2 - 4}$, which simplifies to $\sqrt{5} = \sqrt{9 - 4}$, and finally $\sqrt{5} = \sqrt{5}$. Since both sides of the equation are equal, we can conclude that $x = 3$ is indeed the solution.

Solution:

The solution to the equation $\sqrt{5} = \sqrt{x^2 - 4}$ is $x = 3.

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