Упр.394 ГДЗ Никольский Потапов 9 класс (Алгебра)

а) (2x^(1/2)-y^(1/3))(y^(1/3)+2x^(1/2))
б) (3m^(1/4)-n^(1/4))(n^(1/4)+3m^(1/4))
в) (x^(1/6)-5)(x^(1/6)+5)
г) (3^(1/5)-x^(2/3))(3^(1/5)+x^(2/3))

Используем формулу разности квадратов:

$$ (a-b)(a+b)=a^2-b^2. $$

1. $$ (2x^{1/2}-y^{1/3})(y^{1/3}+2x^{1/2}) =(2x^{1/2})^2-(y^{1/3})^2 =4x-y^{2/3}. $$

2. $$ (3m^{1/4}-n^{1/4})(n^{1/4}+3m^{1/4}) =(3m^{1/4})^2-(n^{1/4})^2 =9m^{1/2}-n^{1/2}. $$

3. $$ (x^{1/6}-5)(x^{1/6}+5) =(x^{1/6})^2-5^2 =x^{1/3}-25. $$

4. $$ (3^{1/5}-x^{2/3})(3^{1/5}+x^{2/3}) =(3^{1/5})^2-(x^{2/3})^2 =3^{2/5}-x^{4/3}. $$

Ответ

а) $$4x-y^{2/3}$$; б) $$9m^{1/2}-n^{1/2}$$; в) $$x^{1/3}-25$$; г) $$3^{2/5}-x^{4/3}$$.