x-2-p-2-xyp-6y-2-0-

Question Number 10204 by gogel last updated on 30/Jan/17

x^{2} p^{2} + x y p - 6 y^{2} = 0

Answered by FilupSmith last updated on 30/Jan/17

solve for x :

a = p^{2}, b = y p, c = - 6 y^{2}

∴ {a x}^{2} + b x + c = 0

∴ x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}

∴ x = \frac{- y p \pm \sqrt{y^{2} p^{2} + 24 p^{2} y^{2}}}{2 p^{2}}

∴ x = \frac{- y p \pm \sqrt{25 p^{2} y^{2}}}{2 p^{2}}

∴ x = \frac{- y p \pm 5 p y}{2 p^{2}}

∴ x = \frac{(- 1 \pm 5) y}{2 p}

x = - \frac{3 y}{p}, \frac{2 y}{p}