Упр.37.32 ГДЗ Мордкович 10-11 класс (Алгебра)

1. 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)

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

Ответ: $$x-1$$

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: $$\sqrt{k}-\sqrt{l}$$