solvefor x,((p-3)(p+5))*x^2-4x+8=0

Lösung

löse nach

x, ((p - 3) (p + 5)) \cdot x^{2} - 4 x + 8 = 0

x = \frac{2 ( - 2 p ^{2} - 4 p + 31 + 1 )}{p ^{2} + 2 p - 15}, x = \frac{2 ( - - 2 p ^{2} - 4 p + 31 + 1 )}{p ^{2} + 2 p - 15}; p \neq = 3, p \neq = - 5

Schritte zur Lösung

((p - 3) (p + 5)) x^{2} - 4 x + 8 = 0

Schreibe

((p - 3) (p + 5)) x^{2} - 4 x + 8

um:

x^{2} p^{2} + 2 x^{2} p - 15 x^{2} - 4 x + 8

x^{2} p^{2} + 2 x^{2} p - 15 x^{2} - 4 x + 8 = 0

Schreibe in der Standard Form

a x^{2} + b x + c = 0

(p^{2} + 2 p - 15) x^{2} - 4 x + 8 = 0

Löse mit der quadratischen Formel

x_{1, 2} = \frac{- ( - 4 ) \pm ( - 4 ) ^{2} - 4 ( p ^{2} + 2 p - 15 ) \cdot 8}{2 ( p ^{2} + 2 p - 15 )}

Vereinfache

(- 4)^{2} - 4 (p^{2} + 2 p - 15) \cdot 8 : 4 - 2 p^{2} - 4 p + 31

x_{1, 2} = \frac{- ( - 4 ) \pm 4 - 2 p ^{2} - 4 p + 31}{2 ( p ^{2} + 2 p - 15 )}; p \neq = 3, p \neq = - 5

Trenne die Lösungen

x_{1} = \frac{- ( - 4 ) + 4 - 2 p ^{2} - 4 p + 31}{2 ( p ^{2} + 2 p - 15 )}, x_{2} = \frac{- ( - 4 ) - 4 - 2 p ^{2} - 4 p + 31}{2 ( p ^{2} + 2 p - 15 )}

x = \frac{- ( - 4 ) + 4 - 2 p ^{2} - 4 p + 31}{2 ( p ^{2} + 2 p - 15 )} : \frac{2 ( - 2 p ^{2} - 4 p + 31 + 1 )}{p ^{2} + 2 p - 15}

x = \frac{- ( - 4 ) - 4 - 2 p ^{2} - 4 p + 31}{2 ( p ^{2} + 2 p - 15 )} : \frac{2 ( - - 2 p ^{2} - 4 p + 31 + 1 )}{p ^{2} + 2 p - 15}

Die Lösungen für die quadratische Gleichung sind:

x = \frac{2 ( - 2 p ^{2} - 4 p + 31 + 1 )}{p ^{2} + 2 p - 15}, x = \frac{2 ( - - 2 p ^{2} - 4 p + 31 + 1 )}{p ^{2} + 2 p - 15}; p \neq = 3, p \neq = - 5

x lo g_{10} (10) (x - 3) = 2

so l v e f or x, 2 x^{2} - 4 x y + 2 y^{2} - 5 x - 5 = 0

so l v e f or x, z^{2} = \frac{324}{972} (x^{2} + y^{2})

so l v e f or x, x^{2} - 3 x - m (m + 3) = 0

so l v e f or x, 3 x^{2} y + 2 y = 5 x