(3x-2)^3-(3x-4)(6x-5)-45x^2=9x^2(3x-5)-10(x+3)-2(6x-1)(6x+1)

Lösung

(3 x - 2)^{3} - (3 x - 4) (6 x - 5) - 45 x^{2} = 9 x^{2} (3 x - 5) - 10 (x + 3) - 2 (6 x - 1) (6 x + 1)

x = 0

Schritte zur Lösung

(3 x - 2)^{3} - (3 x - 4) (6 x - 5) - 45 x^{2} = 9 x^{2} (3 x - 5) - 10 (x + 3) - 2 (6 x - 1) (6 x + 1)

Schreibe

(3 x - 2)^{3} - (3 x - 4) (6 x - 5) - 45 x^{2}

um:

27 x^{3} - 117 x^{2} + 75 x - 28

Schreibe

9 x^{2} (3 x - 5) - 10 (x + 3) - 2 (6 x - 1) (6 x + 1)

um:

27 x^{3} - 117 x^{2} - 10 x - 28

27 x^{3} - 117 x^{2} + 75 x - 28 = 27 x^{3} - 117 x^{2} - 10 x - 28

Verschiebe

28

auf die rechte Seite

27 x^{3} - 117 x^{2} + 75 x = 27 x^{3} - 117 x^{2} - 10 x

Subtrahiere

27 x^{3} - 117 x^{2} - 10 x

von beiden Seiten

27 x^{3} - 117 x^{2} + 75 x - (27 x^{3} - 117 x^{2} - 10 x) = 27 x^{3} - 117 x^{2} - 10 x - (27 x^{3} - 117 x^{2} - 10 x)

Vereinfache

85 x = 0

Teile beide Seiten durch

85

x = 0

2 (3 + 4 x) + 2 x = 10 x + 6

so l v e f or x, 2 x + 5 = y + 12

5 (x + 1) + 3 (x - 2) = 3 (3 x - 2)

y = 9 - (- 1)^{2}

8 x + 1 = 5 x + 5 (2 x - 11)