Question

If a, b, c are in G.P., x and y be the A.M.’s between a, b and b, c respectively, then $\left( \frac { \mathrm { a } } { \mathrm { x } } + \frac { \mathrm { c } } { \mathrm { y } } \right)$ $\left( \frac { b } { x } + \frac { b } { y } \right)$ is equal to

• A. –2
• B. –4
• C. 4
• D. None of these

Answer 1

Answer: (C)

4

Answer 2

b² = ac, x = $\frac { a + b } { 2 }$ , y = $\frac { b + c } { 2 }$

$\frac { 2 b } { a + b } + \frac { 2 b } { b + c }$ = $\frac { 2 \mathrm { ar } } { \mathrm { a } ( 1 + \mathrm { r } ) }$+ = 2

= 4