Question

please help me in solving this question​

Answer 1

Answer:

${a}^{2} ( {p}^{2} + {q}^{2} ) = {r}^{2} ( {b}^{2} + {c}^{2} )$

Step-by-step explanation:

$\alpha + \beta = - \frac{b}{a} \\ \\ \alpha \beta = \frac{c}{a} \\ \\ \frac{1}{ \alpha } + \frac{1}{ \beta } = - \frac{q}{r} \\ \\ \frac{1}{ \alpha \beta } = \frac{r}{p} \\ \\ \frac{ \alpha + \beta }{ \alpha \beta } = - \frac{q}{r} \\ \\ \frac{ - \frac{b}{a} }{ \frac{c}{a} } = - \frac{q}{r} \\ \\ - \frac{b}{a} = - \frac{q}{r} \\ \\ aq = br \\ \\ \\ \\ \\ \\ \frac{c}{a} = \frac{p}{r} \\ \\ ap = cr \\ \\ solving \: these \: equations \: \: {a}^{2} ( {p}^{2} + {q}^{2} ) = {r}^{2} ( {b}^{2} + {c}^{2} )$