Previous Year Questions

(I) (3x - 17/4)² = 81x - 4703/16

=> 9x² - 2 * 3x * 17/4 + 289/16 - 81x + 4703/16 = 0

=> 9x² - 213x/2 + 312 = 0

=> 6x² - 71x + 208 = 0

=> (x - 16/3)(x - 13/2) = 0

=> x = 16/3 and 13/2

(II) y - 125/6 + 99/y = 0

=> 6y² - 125y + 594 = 0

=> (y - 22/3)(y - 27/2) = 0

=> y = 22/3 and 27/2

m = 3/4 * (16/3 + 22/3) = 3/4 * 38/3 = 19/2

And n = 27/2 - 13/2 = 14/2 = 7

Hence, new equation:

(z - 19/2)(z - 7) = 0

=> 2z² - 33z + 133 = 0