(x+5)(2-x)=3sqrt(x^2+x)

Lösung

(x + 5) (2 - x) = 3 x^{2} + x

x \approx 1.21001 \dots, x \approx - 3.41025 \dots

Schritte zur Lösung

(x + 5) (2 - x) = 3 x^{2} + x

Schreibe

(x + 5) (2 - x)

um:

- 3 x - x^{2} + 10

- 3 x - x^{2} + 10 = 3 x^{2} + x

Quadriere beide Seiten:

6 x^{3} + x^{4} - 11 x^{2} - 60 x + 100 = 9 x^{2} + 9 x

6 x^{3} + x^{4} - 11 x^{2} - 60 x + 100 = 9 x^{2} + 9 x

Löse

6 x^{3} + x^{4} - 11 x^{2} - 60 x + 100 = 9 x^{2} + 9 x : x \approx 1.21001 \dots, x \approx - 3.41025 \dots, x \approx 3.37681 \dots, x \approx - 7.17657 \dots

x \approx 1.21001 \dots, x \approx - 3.41025 \dots, x \approx 3.37681 \dots, x \approx - 7.17657 \dots

Überprüfe die Lösungen:

x \approx 1.21001 \dots

Wahr

, x \approx - 3.41025 \dots

Wahr

, x \approx 3.37681 \dots

Falsch

, x \approx - 7.17657 \dots

Falsch

Die Lösungen sind

x \approx 1.21001 \dots, x \approx - 3.41025 \dots

6 y - 17 = 5

so l v e f or n, n = 1 0^{6}

\frac{22}{4 x} = 0

1 - 2 a 1 - a^{2} = 2 a^{2}

- 3 x + 1 + 3 x + 4 = 3