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y=√ (-4x^2+4x+3 / (√ (2x^2-7x+3)))

Решение

y=√ (-4x^2+4x+3 / (√ (2x^2-7x+3)))

1) - 4x^2+4x+3 ≥ 0

4x² - 4x - 3 ≤ 0

D = 16 + 4*4*3 = 64

x₁ = (4 - 8) / 8

x₁ = - 1/2

x₂ = (4 + 8) / 8

x ₂ = 12/8

x ₂ = 3/2 = 1,5

x ∈ [ - 0.5; 1,5]

2) 2x² - 7x + 3 > 0

D = 49 - 4*2*3 = 25

x ₁ = (7 - 5) / 4

x₁ = 1/2

x₁ = 0.5

x₂ = (7 + 5) / 4

x₂ = 3

x ∈ (0,5; 3)

Ответ: x ∈ (0,5; 1,5]