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

Lösung

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

x = \frac{a ^{2}}{2}, x = \frac{b ^{2}}{2}

Schritte zur Lösung

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

Schreibe

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

um:

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

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

Schreibe in der Standard Form

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

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

Löse mit der quadratischen Formel

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

Vereinfache

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

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

Trenne die Lösungen

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

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

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

Die Lösungen für die quadratische Gleichung sind:

x = \frac{a ^{2}}{2}, x = \frac{b ^{2}}{2}

so l v e f or x, f (x + 5) = x^{2} + 4 x + 3

(k - 12) \cdot x^{2} + 2 (k - 12) x + 2 = 0

3 x^{2} + 2 x - 128 = 0

x^{2} + x - (a + 1) (a + 2) = 0

e ln (e) (x^{2} - 3) = 2 x