Упр.37.30 ГДЗ Мордкович 10-11 класс (Алгебра)

а) (1 + c^1/2)^2 — 2c^1/2;
б) (m^1/4 — m^1/3)^2 + 2m^7/12;
в) (x^1/2 — y^1/2)^2 + 2x^1/2 * y^1/2;
г) корень(b) + корень(c) — (b^1/4 + c^1/4)^2.

1. а)

   $$\left(1+c^{\frac12}\right)^2-2c^{\frac12}=1+2c^{\frac12}+c-2c^{\frac12}=1+c.$$

2. б)

   $$\left(m^{\frac14}-m^{\frac13}\right)^2+2m^{\frac7{12}}$$
   $$=m^{\frac12}-2m^{\frac14+\frac13}+m^{\frac23}+2m^{\frac7{12}}$$
   $$=m^{\frac12}-2m^{\frac7{12}}+m^{\frac23}+2m^{\frac7{12}}=m^{\frac12}+m^{\frac23}.$$

3. в)

   $$\left(x^{\frac12}-y^{\frac12}\right)^2+2x^{\frac12}y^{\frac12}$$
   $$=x-2x^{\frac12}y^{\frac12}+y+2x^{\frac12}y^{\frac12}=x+y.$$

4. г)

   $$\sqrt b+\sqrt c-\left(b^{\frac14}+c^{\frac14}\right)^2$$
   $$=b^{\frac12}+c^{\frac12}-\left(b^{\frac12}+2b^{\frac14}c^{\frac14}+c^{\frac12}\right)$$
   $$=-2b^{\frac14}c^{\frac14}=-2\sqrt[4]{bc}.$$

Ответ

а) $$1+c$$; б) $$m^{\frac12}+m^{\frac23}$$; в) $$x+y$$; г) $$-2\sqrt[4]{bc}$$.