find-some-of-all-real-x-such-that-4x-2-15x-17-x-2-4x-12-5x-2-16x-18-2x-2-5x-13-

Question Number 63291 by aliesam last updated on 02/Jul/19

f i n d s o m e o f a l l r e a l x s u c h t h a t

\frac{4 x^{2} + 15 x + 17}{x^{2} + 4 x + 12} = \frac{5 x^{2} + 16 x + 18}{2 x^{2} + 5 x + 13}

Commented by Prithwish sen last updated on 02/Jul/19

\frac{{2 x}^{2} + 5 x + 13}{x^{2} + 4 x + 12} = \frac{{5 x}^{2} + 16 x + 18}{{4 x}^{2} + 15 x + 17}

\frac{x^{2} + x + 1}{x^{2} + 4 x + 12} = \frac{x^{2} + x + 1}{{4 x}^{2} + 15 x + 17}

either x^{2} + x + 1 = 0

or {4 x}^{2} + 15 x + 17 - x^{2} - 4 x - 12 = 0

{3 x}^{2} + 11 x + 5 = 0

∴ x = \frac{- 1 \pm \sqrt{- 3}}{2}, \frac{- 11 \pm \sqrt{61}}{6}

please check

Commented by aliesam last updated on 02/Jul/19

w e l l d o n e s i r

Commented by Prithwish sen last updated on 02/Jul/19

thank you