Answer:
20√37/36
Explanation:
1. Replace x with h and k in the equation:
3h² = 5h + 1 ... (Equation 1)
3k² = 5k + 1 ... (Equation 2)
2. Rearrange both equations so that one side is equal to zero:
3h² - 5h - 1 = 0
3k² - 5k - 1 = 0
3. Solve for h and k using the quadratic formula:
h = [5 ± √(5² - 43(-1))]/(2*3)
= [5 ± √37]/6
k = [5 ± √(5² - 43(-1))]/(2*3)
= [5 ∓ √37]/6
4. Find h² - k:
h² - k = ([5 + √37]/6)² - ([5 - √37]/6)
= (25 + 10√37 + 37)/36 - (25 - 10√37 + 37)/36
= 20√37/36