Упр.10.21 ГДЗ Мерзляк 10 класс Базовый уровень (Алгебра)

1) a+b; 2) a^(1/2)+b^(1/3); 3) a^(3/2)+27; 4) a^(2/3)+b^(2/3).

1. $$a+b=a^{\frac13}+b^{\frac13}=\left(a^{\frac19}+b^{\frac19}\right)\left(a^{\frac29}-a^{\frac19}b^{\frac19}+b^{\frac29}\right).$$

2. $$a^{\frac12}+b^{\frac13}=a^{\frac16}+b^{\frac19}=\left(a^{\frac1{18}}+b^{\frac1{27}}\right)\left(a^{\frac1{9}}-a^{\frac1{18}}b^{\frac1{27}}+b^{\frac2{27}}\right).$$

3. $$a^{\frac32}+27=a^{\frac32}+3^3=\left(a^{\frac12}+3\right)\left(a-3a^{\frac12}+9\right).$$

4. $$a^{\frac23}+b^{\frac23}=a^{\frac29}+b^{\frac29}=\left(a^{\frac1{27}}+b^{\frac1{27}}\right)\left(a^{\frac2{27}}-a^{\frac1{27}}b^{\frac1{27}}+b^{\frac2{27}}\right).$$

Ответ

1. $$a+b=\left(a^{\frac19}+b^{\frac19}\right)\left(a^{\frac29}-a^{\frac19}b^{\frac19}+b^{\frac29}\right).$$

2. $$a^{\frac12}+b^{\frac13}=\left(a^{\frac1{18}}+b^{\frac1{27}}\right)\left(a^{\frac1{9}}-a^{\frac1{18}}b^{\frac1{27}}+b^{\frac2{27}}\right).$$

3. $$a^{\frac32}+27=\left(a^{\frac12}+3\right)\left(a-3a^{\frac12}+9\right).$$

4. $$a^{\frac23}+b^{\frac23}=\left(a^{\frac1{27}}+b^{\frac1{27}}\right)\left(a^{\frac2{27}}-a^{\frac1{27}}b^{\frac1{27}}+b^{\frac2{27}}\right).$$