Упр.10.14 ГДЗ Мерзляк 10 класс Базовый уровень (Алгебра)

1) (5a^0,4+b^0,2)(3a^0,4-4b^0,2); 5) (b^(4/3)-b^(-2/3))^2;
2) (m^0,5+n^0,5)(m^0,5-n^0,5); 6) (x^(1/6)+2)(x^(1/3)-2x^(1/6)+4);
3) (a^(1/3)-5b^(-1/4))(a^(1/3)+5b^(-1/4)); 7) (y^1,5-4y^0,5)^2+8y^2;
4) (m^(1/2)-n^(1/2))^2; 8) (a^(1/8)-1)(a^(1/4)+1)(a^(1/8)+1).

1. $$\left(5a^{0,4}+b^{0,2}\right)\left(3a^{0,4}-4b^{0,2}\right)$$
   $$=15a^{0,8}-20a^{0,4}b^{0,2}+3a^{0,4}b^{0,2}-4b^{0,4}$$
   $$=15a^{0,8}-17a^{0,4}b^{0,2}-4b^{0,4}$$
   $$=15a^{\frac45}-17a^{\frac25}b^{\frac15}-4b^{\frac25}.$$
2. $$\left(m^{0,5}+n^{0,5}\right)\left(m^{0,5}-n^{0,5}\right)=m^{1}-n^{1}=m-n.$$
3. $$\left(a^{\frac13}-5b^{-\frac14}\right)\left(a^{\frac13}+5b^{-\frac14}\right)$$
   $$=a^{\frac23}-25b^{-\frac12}$$
   $$=\sqrt[3]{a^2}-\frac{25}{\sqrt{b}}.$$
4. $$\left(m^{\frac12}-n^{\frac12}\right)^2=m-2\sqrt{mn}+n.$$
5. $$\left(b^{\frac43}-b^{-\frac23}\right)^2=b^{\frac83}-2b^{\frac23}+b^{-\frac43}$$
   $$=\sqrt[3]{b^8}-2\sqrt[3]{b^2}+\frac{1}{\sqrt[3]{b^4}}.$$
6. $$\left(x^{\frac16}+2\right)\left(x^{\frac13}-2x^{\frac16}+4\right)$$
   $$=x^{\frac12}+8$$
   $$=\sqrt{x}+8.$$
7. $$\left(y^{1,5}-4y^{0,5}\right)^2+8y^2$$
   $$=y^3-8y^{1,5+0,5}+16y+8y^2$$
   $$=y^3+16y.$$
8. $$\left(a^{\frac18}-1\right)\left(a^{\frac14}+1\right)\left(a^{\frac18}+1\right)$$
   $$=\left(a^{\frac14}-1\right)\left(a^{\frac14}+1\right)$$
   $$=a^{\frac12}-1$$
   $$=\sqrt{a}-1.$$

Ответ

1) $$15a^{\frac45}-17a^{\frac25}b^{\frac15}-4b^{\frac25}$$
2) $$m-n$$
3) $$\sqrt[3]{a^2}-\frac{25}{\sqrt{b}}$$
4) $$m-2\sqrt{mn}+n$$
5) $$\sqrt[3]{b^8}-2\sqrt[3]{b^2}+\frac{1}{\sqrt[3]{b^4}}$$
6) $$\sqrt{x}+8$$
7) $$y^3+16y$$
8) $$\sqrt{a}-1$$