John J. Hopfield and Geoffrey E. Hinton were awarded the

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

Equation 1: 6x² - 24x + 18 = 0

Equation 2: 5y² - 20y + 15 = 0

A and B are the roots of equation x² - 13x + k = 0. If A - B = 5, what is the value of k?

In each of these questions, two equations (I) and (II) are given.You have to solve both the equations and give answer   

I. 63x² + 148x + 77 = 0

II. 21y² + 89y + 88 = 0

I. x² - 33x + 270 = 0

II. y² - 41y + 414 = 0

What are the coordinates of the point which divides the line joining (-1, 7) and (4, 3) in the ratio 2:3?

If α, β are the roots of the equation x² – px + q = 0, then the value of α²+β²+2αβ is 

I. 3y² - 20y + 25 = 0

II. 3x² - 8x + 5 = 0

I: 2x² - 8x + 6 = 0

II: 3y² - 12y + 9 = 0

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

Equation 1: x² - 34x + 288 = 0

Equation 2: y² - 29y + 210 = 0