Упр.63 ГДЗ Алимов 10-11 класс (Алгебра)

1)x1/2 + x;
2) (ab)1/3 + (ac)1/3;
3) y3/4 — y1/3;
4) 12xy1/2 — 3×1/2y.

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

2. $$\left(ab\right)^{\frac13}+\left(ac\right)^{\frac13}=a^{\frac13}b^{\frac13}+a^{\frac13}c^{\frac13}=a^{\frac13}\left(b^{\frac13}+c^{\frac13}\right).$$

3. $$y^{\frac34}-y^{\frac13}=y^{\frac{9}{12}}-y^{\frac{4}{12}}=y^{\frac{4}{12}}\left(y^{\frac{5}{12}}-1\right)=y^{\frac13}\left(y^{\frac{5}{12}}-1\right).$$

4. $$12xy^{\frac12}-3x^{\frac12}y=3x^{\frac12}y^{\frac12}\left(4x^{\frac12}-y^{\frac12}\right).$$

Ответ

1) $$x^{\frac12}\left(1+x^{\frac12}\right)$$
2) $$a^{\frac13}\left(b^{\frac13}+c^{\frac13}\right)$$
3) $$y^{\frac13}\left(y^{\frac{5}{12}}-1\right)$$
4) $$3x^{\frac12}y^{\frac12}\left(4x^{\frac12}-y^{\frac12}\right)$$