SSC CGL 2018 PYQ — Question 86

The correct answer is option 2 i.e. (Q² - 2PR)(R+P)/PR²

a and b are the roots of (Px² – Qx + R = 0):

a + b = Q/P

a × b = R/P

1/a² + 1/b² + a/b + b/a = (a² + b²)/(ab)² + (a² + b²)/ab  .......(1)

(a + b)² = Q²/P² 

⇒ a² + b² = Q²/P² - 2R/P

⇒ a² + b² = (Q² - 2PR)/P²

Putting this in equation (1):

1/a² + 1/b² + a/b + b/a

= (Q² - 2PR)/(P² × R²/P²) + (Q² - 2PR)/(P² × R/P)

= (Q² - 2PR)/R² + (Q² - 2PR)/PR

= (Q² - 2PR)(R + P)/PR²