4x2-4x+33=8√(12+16x-16x2)

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вопрос

4x^2 - 4x + 33 = 8√(12 + 16x - 16x^2)

First, let's simplify the right side of the equation:

8√(12 + 16x - 16x^2) = 8√(12 - 16x^2 + 16x)
= 8√(4(3 - 4x^2 + 4x))
= 8 * 2√(3 - 4x^2 + 4x)
= 16√(3 - 4x^2 + 4x)

Now, we can substitute this back into the original equation:

4x^2 - 4x + 33 = 16√(3 - 4x^2 + 4x)

Next, square both sides of the equation to eliminate the square root:

(4x^2 - 4x + 33)^2 = (16√(3 - 4x^2 + 4x))^2
16x^4 - 32x^3 + 66x^2 - 32x + 1089 = 256(3 - 4x^2 + 4x)

Then, expand and simplify:

16x^4 - 32x^3 + 66x^2 - 32x + 1089 = 768 - 1024x^2 + 1024x

Rearrange terms:

16x^4 - 32x^3 + 1090x^2 - 1056x + 321 = 0

Therefore, the solution to the equation is 16x^4 - 32x^3 + 1090x^2 - 1056x + 321 = 0.