Question

решите уравнение:
$x \sqrt[3]{x} - 4 \sqrt[3]{x ^{2} } + 4 = 0$
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Answer 1

$x\cdot \sqrt[3]{x}-4\sqrt[3]{x^2}+4=0\\\\\sqrt[3]{x^4}-4\sqrt[3]{x^2}+4=0\\\\\left ( \sqrt[3]{x^2}-2 \right )^2=0\\\\\sqrt[3]{x^2}=2\\\\x=\pm 2\sqrt{2}$

Answer 2

x∛x - 4∛x² + 4 = 0

(∛x²)² - 4∛x² + 4 = 0

∛x² = t

t² - 4t + 4 = 0

(t - 2)² = 0

∛x² = t= 2

x² = 8

x = +- √8 = +- 2√2

ответ +-2√2