Tìm x

To solve this equation, we need to simplify each square root expression and then combine like terms.

Starting with the left side of the equation:
√(x^2 - 3x + 2) + √(x + 3)

We can factor the first square root expression:
√((x - 1)(x - 2)) + √(x + 3)

Now, let's simplify the second square root expression:
√((x - 1)(x - 2)) + √((x - 1)(x + 3))

Notice that both square root expressions have a common factor of (x - 1). We can factor it out:
√(x - 1) * √(x - 2) + √(x - 1) * √(x + 3)

Now, we can combine the like terms:
√(x - 1) * (√(x - 2) + √(x + 3))

Moving on to the right side of the equation:
√(x - 2) + √(x^2 + 2x - 3)

We can factor the second square root expression:
√(x - 2) + √((x - 1)(x + 3))

Now, we can see that both square root expressions have a common factor of √(x - 2). We can factor it out:
√(x - 2) * (1 + √(x - 1)(x + 3))

Now, our equation becomes:
√(x - 1) * (√(x - 2) + √(x + 3)) = √(x - 2) * (1 + √(x - 1)(x + 3))

To solve for x, we can square both sides of the equation:
(√(x - 1) * (√(x - 2) + √(x + 3)))^2 = (√(x - 2) * (1 + √(x - 1)(x + 3)))^2

Expanding both sides:
(x - 1) * (√(x - 2))^2 + 2√(x - 1) * √(x - 2) * √(x + 3) + (x - 1) * (√(x + 3))^2 = (x - 2) * (1 + √(x - 1)(x + 3))^2

Simplifying:
(x - 1) * (x - 2) + 2√(x - 1) * √(x - 2) * √(x + 3) + (x - 1) * (x + 3) = (x - 2) * (1 + √(x - 1)(x + 3))^2

Expanding further:
(x^2 - 3x + 2) + 2√(x - 1) * √(x - 2) * √(x + 3) + (x^2 + 2x - 3) = (x - 2) * (1 + √(x - 1)(x + 3))^2

Now, we can simplify the square roots:
(x^2 - 3x + 2) + 2√((x - 1)(x - 2)(x + 3)) + (x^2 + 2x - 3) = (x - 2) * (1 + √(x - 1)(x + 3))^2

Combining like terms:
2x^2 - x + 1 + 2√((x - 1)(x - 2)(x + 3)) = (x - 2) * (1 + √(x - 1)(x + 3))^2

At this point, it becomes difficult to solve for x algebraically. We can use numerical methods or graphing to find approximate solutions.