Упр.8.33 ГДЗ Мордковича 11 класс профильный уровень (Алгебра)

• а) $$(x^{1/4}+1)(x^{1/4}-1)(x^{1/2}+1)$$; б) $$(k^{1/4}+l^{1/4})(k^{1/8}+l^{1/8})(k^{1/8}-l^{1/8})$$.

а) $$\left(x^{\frac14}+1\right)\left(x^{\frac14}-1\right)\left(x^{\frac12}+1\right)=\left(x^{\frac12}-1\right)\left(x^{\frac12}+1\right)=x-1.$$

б) $$\left(k^{\frac14}+l^{\frac14}\right)\left(k^{\frac18}+l^{\frac18}\right)\left(k^{\frac18}-l^{\frac18}\right)=\left(k^{\frac14}+l^{\frac14}\right)\left(k^{\frac14}-l^{\frac14}\right)=k^{\frac12}-l^{\frac12}=\sqrt{k}-\sqrt{l}.$$

Ответ: а) $$x-1$$; б) $$\sqrt{k}-\sqrt{l}$$.