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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-




Question Number 74412 by ajfour last updated on 24/Nov/19
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..?
$${a},{b},{c}\:{are}\:{given}\:{real}\:{constants}. \\ $$$${p},{q},{r},{t}\:{are}\:{unknowns}\:{from}\:{which} \\ $$$${we}\:{can}\:{choose}\:{values}\:{of}\:{two}\:{of} \\ $$$${them}\:\left({non}\:{zero}\right)\:{and}\:{have}\:{to}\: \\ $$$${determine}\:{the}\:{other}\:{two}\:\left({non}\:{zero}\right), \\ $$$${obeying}\:\:{two}\:{equations}\:{given}\:{below} \\ $$$$\:{p}^{\mathrm{2}} +{q}\left(\mathrm{1}+{bq}\right){t}^{\mathrm{2}} +{q}\left({ap}+{br}\right){t} \\ $$$$\:\:\:\:\:+{r}\left(\mathrm{1}+{bq}\right){t}+{r}\left({ap}+{br}\right)\:=\:\mathrm{0} \\ $$$${pt}+{q}\left({a}+{cq}\right){t}^{\mathrm{2}} +{r}\left({a}+{cq}\right){t} \\ $$$$\:\:\:\:+{cqrt}+{cr}^{\mathrm{2}} =\:\mathrm{0} \\ $$$${Can}\:{this}\:{be}\:{done}\:{solving}\:{a} \\ $$$${quadratic}\:{eq}.\:{and}\:{none}\:{higher}..? \\ $$

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