Question

4. Скоротіть дріб: (12 ^ (1/3) - 4 ^ (1/3))/(6 ^ (1/3) - 2 ^ (1/3))

Answer 1

Ответ: ∛2.

Объяснение:

 $\displaystyle\\\frac{12^\frac{1}{3} -4^\frac{1}{3} }{6^\frac{1}{3}-2^\frac{1}{3} }=\frac{(4*3)^\frac{1}{3}-4^\frac{1}{3} }{(2*3)^\frac{1}{3}-2^\frac{1}{3} } =\frac{4^\frac{1}{3} *3^\frac{1}{3}-4^\frac{1}{3} }{2^\frac{1}{3} *3^\frac{1}{3}-2^\frac{1}{3} } =\frac{4^\frac{1}{3}(3^\frac{1}{3}-1) }{2^\frac{1}{3} (3^\frac{1}{3}-1) }=\frac{4^\frac{1}{3} }{2^\frac{1}{3} }=(\frac{4}{2})^\frac{1}{3}=\\\\=2^\frac{1}{3} =\sqrt[3]{2} .$