Final answer:
To solve the equation x² - 4x - 3 = 0, use the quadratic formula and simplify to find the largest value of x.
Step-by-step explanation:
To solve the equation x² - 4x - 3 = 0, we can use the quadratic formula. The quadratic formula is x = (-b ± sqrt(b^2 - 4ac))/(2a), where a, b, and c are the coefficients of the equation. In this case, a = 1, b = -4, and c = -3. Plugging these values into the quadratic formula, we get x = (4 ± sqrt((-4)^2 - 4(1)(-3)))/(2(1)). Simplifying further, we have x = (4 ± sqrt(16 + 12))/2. This becomes x = (4 ± sqrt(28))/2. Taking the square root of 28, we get x = (4 ± sqrt(4*7))/2. This simplifies to x = (4 ± 2sqrt(7))/2, which can be further simplified as x = 2 ± sqrt(7). Since we're looking for the largest value of x, our final answer is x = 2 + sqrt(7).