If the slope of chord PQ of f(x)`=x^(3)-2x^(-3)+10` is 9, then relation between the AM (A) and GM (G) of abscissae of points P and Q is -

Options

A. `9G^(2)-(7A^(2)-G^(2))(G^(6)+2)=0`
B. `6G^(6)-(7A^(2)-G^(2))(G^(6)+2)=0`
C. `9G^(6)-(4A^(2)-G^(2))(G^(6)+2)=0`
D. `6G^(6)-(4A^(2)-G^(2))(G^(6)+2)=0`

Answer

C

Explanation

Let `y=f(x)=x^(3)-2x^(-3)+10`
`:. y_(1)-y_(2)=(x_(1)^(2)-x_(2)^(3))+2(x_(2)^(-3)-x_(1)^(-3))`
`" "= (x_(1)^(3)-x_(2)^(3))+2((x_(1)^(3)-x_(2)^(3))/((x_(1) x_(2))^(3)))`
`(y_(1)-y_(2))/(x_(1)-x_(2))=(x_(1)^(2)+x_(2)^(2)+x_(1)x_(2))(1+(2)/((x_(1) x_(2))^(3)))`
`rArr([(x_(1)+x_(2))^(2)-x_(1)x_(2)][(x_(1)x_(2))^(3)+2])/((x_(1)-x_(2))^(3))`
`((4A^(2)-G^2)(G^(6)+2))/(G^(6))`
`rArr9G^(6)-(4A^(2)-G^(2))(G^(6)+2)=0`