Select the next number in the series. 52, 53, 57,

For 3x² − 10x − 8 = 0, find (1/α + 1/β).

In the question, two equations I and II are given. You have to solve both the equations to establish the correct relation between x and y.

I. 2x² - 9 x + 9 = 0 

II. 2y² - 7 y + 3 = 0

I. 8x² - 74x + 165 = 0

II. 15y² - 38y + 24 = 0

I. 3x² - 16x - 12 = 0

II. 2y² + 11y + 9 = 0

For what values of k does the equation x² – (k+1)x + k = 0 have two distinct real roots, both greater than 1?

l. x² - 16x + 64 = 0

II. y² = 64

I. 66x² - 49x + 9 = 0

II. 46y² - 37y - 30 = 0

I. 3p² - 17p + 22 = 0

II. 5q² - 21q + 22 = 0