Final answer:
Solve the given equation by making a substitution for d² with a new variable, solve the resulting quadratic equation, and then calculate the square root of the solutions to find the values of d.
Step-by-step explanation:
To solve the equation d²(d²-3) = 2d² + 3, we can make an appropriate substitution to simplify the equation. Let's substitute d² with a new variable, say u. The equation can then be written as u(u-3) = 2u + 3.
Expanding the left side of the equation gives us: u² - 3u = 2u + 3. Moving all terms to one side, we get: u² - 5u - 3 = 0. This is a standard quadratic equation in terms of u. using the quadratic formula, u = √(−5² - 4 × 1 × (−3)) / 2 × 1. Calculating the values, we solve for u, and then substitute back to find the values of d by calculating the square root of u.