If the slope of one of the lines represented by `ax^(2)+2hxy+by^(2)=0` is the square of the other , then `(a+b)/(h)+(8h^(2))/(ab)=`

Answer

6

Explanation

`alpha+alpha^(2)=(-2h)/(b) .........(1)`
And `alpha.alpha^(2)=a/b rArr alpha=(a/b)^(1//3) ........(2)`
Substituting value of `alpha` from (ii) in (i), we get : `(a/b)^(1//3)+(a/b)^(2//3) alpha=(-2h)/(b)`
Cubing both sides, we get : `a/b+a^(2)/b^(2)+3(a/b) [(a/b)^(1//3)+(a/b)^(2//3)]=(-8h^(3))/(b^(3))`
`rArr a/b+a^(2)/b^(2)-(6ah)/(b^(2))=-(8h^(3))/(b^(3)) rArr ab^(2)+a^(2)b-6abh =-8h^(3)`
`rArr (b+a)/(h)+(8h^(2))/(ab)=6`