Previous Year Questions

Equation I:

N = 3 [The lowest odd prime number]

N² = 9

A² - 21A + 228 = 0

A² - 12A - 19A + 228 = 0

A (A - 12) - 19 (A - 12) = 0

(A - 19) (A - 12) = 0

A = 19, 12

If M = 19 and P = 12

4X² - 12X - (19² + 9) = 0

4X² - 12X - 370 = 0

2X² - 6X - 185 = 0

X = (6 ± √1516)/4 [Not satisfied]

If M = 12 and P = 19

4X² - 19X - (12² + 9) = 0

4X² - 19X - 153 = 0

4X² - 36X + 17X - 153 = 0

4X (X - 9) + 17 (X - 9) = 0

(4X + 17) (X - 9) = 0

X = - 4.25, 9 [Satisfied]

Equation II:

Y - √N² = (8M - P + 7)/3Y

Y - √9 = (8 * 12 - 19 + 7)/3Y

Y - 3 = 84/3Y

Y - 3 = 28/Y

Y² - 3Y = 28

Y² - 3Y - 28 = 0

Y² - 7Y + 4Y - 28 = 0

Y (Y - 7) + 4 (Y - 7) = 0

(Y + 4) (Y - 7) = 0

Y = -4, 7

17P - 53N + 19M - 9 * the largest roots of equation II

=> 17 * 19 - 53 * 3 + 19 * 12 - 9 * 7

=> 323 - 159 + 228 - 63

=> 551 - 222

=> 329