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I. 3p² - 14p + 15 = 0

II. 15q²  - 34q + 15 = 0

I. 6p² + 17p + 12 = 0

II. 12q² - 25q + 7 = 0

Solve the quadratic equations and determine the relation between x and y:

Equation 1: x² - 41x + 400 = 0

Equation 2: y² - 41y + 420 = 0

I. 5x + 2y = 31

II. 3x + 7y = 36

I: √(100 x⁴ + 125x⁴) + 7x + 4^1/2 = -4x

1.3wx = 40 – wy

2. b² = 2b + p

3. d² + d = q

Now, observe the given conditions:

I. p² - 10p +21 = 0

II. q² + q -12 = 0

I. x³ = 1728

II. y² – 15y + 56 = 0

Solve the quadratic equations and determine the relation between x and y:

Equation 1: x² - 50x + 600 = 0

Equation 2: y² - 51y + 630 = 0

I. 2y² - 3y – 14 = 0

II. 3x² - 7x + 4 = 0