Since,(α+√β) and (α−√β) are the roots of the equation x2+px+q=0 ∴ Sum of roots =−p ⇒(α+√β)+(α−√β)=−p ⇒2α=−p⇒α=−‌
p
2
and product of roots = q (α+√β)(α−√β)=q ⇒α2−β=q
⇒β=α2−q=(−‌
p
2
)2−q=‌
p2
4
−q
⇒p2−4q=4β ∴ The given equation (p2−4q)(p2x2+4px)−16q=0 4β(p2x2+4px)−16(α2−β)=0 [α2−β=q] β(4α2x2−8αx)−4(α2−β)=0 α2βx2−2αβx+β=α2 ⇒(αx√β−√β)2=α2 ⇒αx√β−√β=±α ∴x=‌