√2х^2-8х+6+√4х-х^2-3<х-1

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To solve this inequality, we need to first combine like terms and simplify the expression:

√(2х^2 - 8х + 6) + √(4х - х^2 - 3) < х - 1

Next, let's simplify each square root term:

√(2х^2 - 8х + 6) = √2(х^2 - 4х + 3) = √2(x - 3)(x - 1)
√(4х - х^2 - 3) = √(4 - (x - 3)(x+1)) = 2 - (x - 3)

After simplifying, the inequality becomes:

√2(x - 3)(x - 1) + 2 - (x - 3) < x - 1

Expand the expression to get:

√2x^2 - √2x - 2√2x + 2√2 - x + 3 + 2 - x + 3 < x - 1

Simplify further:

√2x^2 - 3x + 4√2 + 5 < x - 1

Now, we need to isolate x term on one side and all constants on the other:

√2x^2 - 3x + 4√2 + 5 < x - 1

Subtract x from both sides:

√2x^2 - 4x + 4√2 + 5 < -1

Now, rewrite the inequality as a quadratic inequality:

√2x^2 - 4x + 4√2 + 5 + 1 < 0
√2x^2 - 4x + 4√2 + 6 < 0

At this point, we can graph the quadratic function or use the quadratic formula to determine the solutions, depending on the level of rigor needed for the solution. Let me know if you need further steps to solve this inequality.