Question

Rozwiąż równanie

x^2= pierwiastek z 2* x^5

Answer 1

 

Answer 2

I. Jeżeli mamy:

x² = √(2x⁵) I()²             Z: 2x⁵ ≥0

x⁴ = 2x⁵                            x ≥ 0

x⁴-2x⁵ = 0

x⁴(1-2x) = 0

x⁴ = 0   => x = 0

lub

1-2x = 0

-2x = -1  /:(-2)

x = 1/2

Odp. x = 0   v    x = 1/2

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II. Jeżeli mamy:

x² = √2·x⁵

x²-√2x⁵ = 0

x²(1-√2x³) = 0

x² = 0   => x = 0

lub

1-2x³ = 0

-2x³ = -1  /:(-2)

x³ = 1/√2 = √(1/2)

x³ = (1/2)¹/²  I()∛

x = [(1/2)¹/²]¹/³

x = (1/2)¹/⁶

x = ⁶√(½)

Odp. x = 0   v   x = ⁶√(½)

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