Question

1. solve the equation. che

\\(\sqrt{m + 3} = \sqrt{2m + 1}\\)

Explanation:

Step1: Square both sides to eliminate roots

$$(\sqrt{m+3})^2 = (\sqrt{2m+1})^2$$
$$m+3 = 2m+1$$

Step2: Isolate variable $m$

$$3 - 1 = 2m - m$$

Step3: Simplify to solve for $m$

$$2 = m$$

Step4: Verify solution in original equation

Left side: $\sqrt{2+3}=\sqrt{5}$
Right side: $\sqrt{2(2)+1}=\sqrt{5}$
Both sides are equal, so solution is valid.

Answer:

$m=2$