Question

The Harmonic Mean of roots of equation

(5 + $\sqrt { 2 }$) x² – (4 + $\sqrt { 5 }$ ) x + 8 + 2 $\sqrt { 5 }$ = 0 is

• A. 2
• B. 6
• C. 4
• D. 8

Answer 1

Answer: (C)

4

Answer 2

H.M. of a, b = $\frac { 2 \alpha \beta } { \alpha + \beta }$ = $\frac { 2 \times \frac { ( 8 + 2 \sqrt { 5 } ) } { 5 + \sqrt { 2 } } } { \left( \frac { 4 + \sqrt { 5 } } { 5 + \sqrt { 2 } } \right) }$

= $\frac { 2 \times 2 ( 4 + \sqrt { 5 } ) } { 4 + \sqrt { 5 } }$ = 4