4x^2-2(a^4-b^4)x+a^2b^2=0

Lösung

4 x^{2} - 2 (a^{4} - b^{4}) x + a^{2} b^{2} = 0

x = \frac{2 a ^{4} - 2 b ^{4} + ( - 2 a ^{4} + 2 b ^{4} ) ^{2} - 16 a ^{2} b ^{2}}{8}, x = \frac{2 a ^{4} - 2 b ^{4} - ( - 2 a ^{4} + 2 b ^{4} ) ^{2} - 16 a ^{2} b ^{2}}{8}

Schritte zur Lösung

4 x^{2} - 2 (a^{4} - b^{4}) x + a^{2} b^{2} = 0

Schreibe

4 x^{2} - 2 (a^{4} - b^{4}) x + a^{2} b^{2}

um:

4 x^{2} - 2 a^{4} x + 2 b^{4} x + a^{2} b^{2}

4 x^{2} - 2 a^{4} x + 2 b^{4} x + a^{2} b^{2} = 0

Schreibe in der Standard Form

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

4 x^{2} + (- 2 a^{4} + 2 b^{4}) x + a^{2} b^{2} = 0

Löse mit der quadratischen Formel

x_{1, 2} = \frac{- ( - 2 a ^{4} + 2 b ^{4} ) \pm ( - 2 a ^{4} + 2 b ^{4} ) ^{2} - 4 \cdot 4 a ^{2} b ^{2}}{2 \cdot 4}

Vereinfache

(- 2 a^{4} + 2 b^{4})^{2} - 4 \cdot 4 a^{2} b^{2} : (- 2 a^{4} + 2 b^{4})^{2} - 16 a^{2} b^{2}

x_{1, 2} = \frac{- ( - 2 a ^{4} + 2 b ^{4} ) \pm ( - 2 a ^{4} + 2 b ^{4} ) ^{2} - 16 a ^{2} b ^{2}}{2 \cdot 4}

Trenne die Lösungen

x_{1} = \frac{- ( - 2 a ^{4} + 2 b ^{4} ) + ( - 2 a ^{4} + 2 b ^{4} ) ^{2} - 16 a ^{2} b ^{2}}{2 \cdot 4}, x_{2} = \frac{- ( - 2 a ^{4} + 2 b ^{4} ) - ( - 2 a ^{4} + 2 b ^{4} ) ^{2} - 16 a ^{2} b ^{2}}{2 \cdot 4}

x = \frac{- ( - 2 a ^{4} + 2 b ^{4} ) + ( - 2 a ^{4} + 2 b ^{4} ) ^{2} - 16 a ^{2} b ^{2}}{2 \cdot 4} : \frac{2 a ^{4} - 2 b ^{4} + ( - 2 a ^{4} + 2 b ^{4} ) ^{2} - 16 a ^{2} b ^{2}}{8}

x = \frac{- ( - 2 a ^{4} + 2 b ^{4} ) - ( - 2 a ^{4} + 2 b ^{4} ) ^{2} - 16 a ^{2} b ^{2}}{2 \cdot 4} : \frac{2 a ^{4} - 2 b ^{4} - ( - 2 a ^{4} + 2 b ^{4} ) ^{2} - 16 a ^{2} b ^{2}}{8}

Die Lösungen für die quadratische Gleichung sind:

x = \frac{2 a ^{4} - 2 b ^{4} + ( - 2 a ^{4} + 2 b ^{4} ) ^{2} - 16 a ^{2} b ^{2}}{8}, x = \frac{2 a ^{4} - 2 b ^{4} - ( - 2 a ^{4} + 2 b ^{4} ) ^{2} - 16 a ^{2} b ^{2}}{8}

\frac{( 6 x ^{2} )}{5} = 4.8

\frac{( n ( n + 6 ) )}{12} = 18000

\frac{2 x ^{2}}{16} = 2^{3} x

2.2 x^{2} - 8.8 x = 0

so l v e f or x, x^{2} - y^{4} = 2035