3 Gleichungen Lösungsmengen

Question

Leider bereiten mir diese Gleichungen Kopfschmerzen. Ich wäre für die Lösungswege sehr dankbar.

1. -3^(3/2) • x^(1/2) + 9 = 0

2. 2x⁹ + 128⁶ = 0

3. (1/3)x² + (1/3)x -10= 0

Grüße

Answer 1

3 Gleichungen Lösungsmengen

Answer 2

- 3^{3/2}·x^{1/2} + 9 = 0

- 3^{3/2}·x^{1/2} = -9

x^{1/2} = 9 / 3^{3/2}

x = 81 / 3^3 = 81/27 = 3

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2·x^9 + 128^6 = 0

2·x^9 = - 128^6

2·x^9 = - (2^7)^6

2·x^9 = - 2^42

x^9 = - 2^41

x = - 2^{41/9}

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1/3·x^2 + 1/3·x - 10 = 0

x^2 + x - 30 = 0

(x - 5)·(x + 6) = 0

x = -6 ∨ x = 5