Question

решить уравнение ³√8х=√2*³√2

Answer 1

$sqrt[3]{8x} = sqrt{2} sqrt[3]{2} \ sqrt[3]{8x} = sqrt[6]{ {2}^{3} } sqrt[6]{ {2}^{2} } \ sqrt[3]{8x} = sqrt[6]{ {2}^{3} {2}^{2} } \ sqrt[3]{8x} = sqrt[6]{ {2}^{5} } \ ( sqrt[3]{8x} ) {}^{3} = ( sqrt[6]{32} ) {}^{3} \ 8x = sqrt{32} \ x = frac{ sqrt{32} }{8} \ x = frac{4 sqrt{2} }{8} \ x = frac{ sqrt{2} }{2}$