Question

Sqrt(2x-3)=sqrt(5+x)

Answer 1

2x-3=5+x
x=8
Можно проверить или найти ОДЗ.
Вопросы есть?
1) Проверка:
$\sqrt{2*8-3}= \sqrt{5+8}$
$\sqrt{16-3}= \sqrt{13}$
$\sqrt{13} = \sqrt{13}$
верно.
2) ОДЗ:
$\left \{ {{2x-3 \geq 0} \atop {5+x \geq 0}} \right.$
$\left \{ {{x \geq 1,5} \atop {x \geq -5}} \right.$
=> $x \geq 1,5$

Answer 2

To solve the equation √(2x - 3) = √(5 + x), we'll need to follow these steps:

Step 1: Square both sides of the equation to eliminate the square roots. Step 2: Solve for x. Step 3: Check the solutions in the original equation to ensure they are valid.

Let's go through these steps:

Step 1: (√(2x - 3))^2 = (√(5 + x))^2 2x - 3 = 5 + x

Step 2: Subtract x from both sides: 2x - x - 3 = 5 x - 3 = 5

Add 3 to both sides: x = 5 + 3 x = 8

Step 3: Now, let's check if the solution x = 8 satisfies the original equation: √(2(8) - 3) = √(5 + 8) √(16 - 3) = √13 √13 = √13

Since the equation is true for x = 8, this is indeed a valid solution.

So, the solution to the equation √(2x - 3) = √(5 + x) is x = 8.