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if S8/S4=97/81 in a G.P. Prove that r=2/3

$Given \frac{S_{8}}{S_{4}} = \frac{97}{81} \frac{\frac{a (1 - r^{8})}{1 - r}}{\frac{a (1 - r^{8})}{1 - r}} = \frac{97}{81} \frac{1 - r^{8}}{1 - r^{4}} = \frac{97}{81} 81 - 81 r^{8} = 97 - 97 r^{4} 81 r^{8} - 97 r^{4} + 16 = 0 Using quadratic formula r^{4} = \frac{97 \pm \sqrt{97^{2} - 4 (81) (16)}}{81 \times 2} r^{4} = \frac{97 \pm \sqrt{9409 - 5184}}{162} r^{4} = \frac{97 \pm \sqrt{4225}}{162} = \frac{97 \pm 65}{162} r^{4} = \frac{162}{162}, \frac{32}{162} r^{4} = 1, \frac{16}{81} \Rightarrow r = 1, \frac{2}{3}$

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