a,b,c are given real constants. p,q,r,t are unknowns from which we can choose values of two of them (non zero) and have to determine the other two (non zero), obeying two equations given below p^2 +q(1+bq)t^2 +q(ap+br)t +r(1+bq)t+r(ap+br) = 0 pt+q(a+cq)t^2 +r(a+cq)t +cqrt+cr^2 = 0 Can this be done solving a quadratic eq. and none higher..?


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Question Number 74412 by ajfour last updated on 24/Nov/19

$a, b, c a r e g i v e n r e a l c o n s t a n t s .$ $p, q, r, t a r e u n k n o w n s f r o m w h i c h$ $w e c a n c h o o s e v a l u e s o f t w o o f$ $t h e m (n o n z e r o) a n d h a v e t o$ $d e t e r m i n e t h e o t h e r t w o (n o n z e r o),$ $o b e y i n g t w o e q u a t i o n s g i v e n b e l o w$ $p^{2} + q (1 + b q) t^{2} + q (a p + b r) t$ $+ r (1 + b q) t + r (a p + b r) = 0$ $p t + q (a + c q) t^{2} + r (a + c q) t$ $+ c q r t + {c r}^{2} = 0$ $C a n t h i s b e d o n e s o l v i n g a$ $q u a d r a t i c e q . a n d n o n e h i g h e r . . ?$
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