Упр.104 Вариант 1 Дидактические материалы ГДЗ Мерзляк Полонский 8 класс (Алгебра)

1) 6/v17; 5) (x-3)/v(x-3); 9) (x-4)/(v(x+5)-3);
2) 12/v3; 6) 1/(v26-1); 10) (x^2+4x)/(v(x+8)-2);
3) 30/(7v5); 7) 35/(v37+v2); 11) (x^2-16)/(3-v(x+5));
4) a^3/(bva); 8) 16/(v47-v15); 12) x/(v(3-x)+v(3+2x)).

1. $$\frac{6}{\sqrt{17}}=\frac{6\sqrt{17}}{\sqrt{17}\sqrt{17}}=\frac{6\sqrt{17}}{17}$$
2. $$\frac{12}{\sqrt{3}}=\frac{12\sqrt{3}}{\sqrt{3}\sqrt{3}}=\frac{12\sqrt{3}}{3}=4\sqrt{3}$$
3. $$\frac{30}{7\sqrt{5}}=\frac{30\sqrt{5}}{7\cdot 5}=\frac{6\sqrt{5}}{7}$$
4. $$\frac{a^3}{b\sqrt{a}}=\frac{a^3\sqrt{a}}{ba}=\frac{a^2\sqrt{a}}{b}$$
5. $$\frac{x-3}{\sqrt{x-3}}=\frac{(x-3)\sqrt{x-3}}{x-3}=\sqrt{x-3}$$
6. $$\frac{1}{\sqrt{26}-1}=\frac{1(\sqrt{26}+1)}{(\sqrt{26}-1)(\sqrt{26}+1)}=\frac{\sqrt{26}+1}{26-1}=\frac{\sqrt{26}+1}{25}$$
7. $$\frac{35}{\sqrt{37}+\sqrt{2}}=\frac{35(\sqrt{37}-\sqrt{2})}{(\sqrt{37}+\sqrt{2})(\sqrt{37}-\sqrt{2})}=\frac{35(\sqrt{37}-\sqrt{2})}{37-2}=\sqrt{37}-\sqrt{2}$$
8. $$\frac{16}{\sqrt{47}-\sqrt{15}}=\frac{16(\sqrt{47}+\sqrt{15})}{(\sqrt{47}-\sqrt{15})(\sqrt{47}+\sqrt{15})}=\frac{16(\sqrt{47}+\sqrt{15})}{47-15}=\frac{\sqrt{47}+\sqrt{15}}{2}$$
9. $$\frac{x-4}{\sqrt{x+5}-3}=\frac{(x-4)(\sqrt{x+5}+3)}{(\sqrt{x+5}-3)(\sqrt{x+5}+3)}=\frac{(x-4)(\sqrt{x+5}+3)}{x+5-9}=\sqrt{x+5}+3$$
10. $$\frac{x^2+4x}{\sqrt{x+8}-2}=\frac{(x^2+4x)(\sqrt{x+8}+2)}{(\sqrt{x+8}-2)(\sqrt{x+8}+2)}$$
    $$=\frac{x(x+4)(\sqrt{x+8}+2)}{x+8-4}=x(\sqrt{x+8}+2)$$
11. $$\frac{x^2-16}{3-\sqrt{x+5}}=\frac{(x^2-16)(3+\sqrt{x+5})}{(3-\sqrt{x+5})(3+\sqrt{x+5})}$$
    $$=\frac{(x-4)(x+4)(3+\sqrt{x+5})}{9-(x+5)}=\frac{(x-4)(x+4)(3+\sqrt{x+5})}{4-x}$$
    $$=-(x+4)(3+\sqrt{x+5})$$
12. $$\frac{x}{\sqrt{3-x}+\sqrt{3+2x}}=\frac{x(\sqrt{3-x}-\sqrt{3+2x})}{(\sqrt{3-x}+\sqrt{3+2x})(\sqrt{3-x}-\sqrt{3+2x})}$$
    $$=\frac{x(\sqrt{3-x}-\sqrt{3+2x})}{(3-x)-(3+2x)}=\frac{x(\sqrt{3-x}-\sqrt{3+2x})}{-3x}$$
    $$=\frac{\sqrt{3+2x}-\sqrt{3-x}}{3}$$

Ответ

1. $$\frac{6\sqrt{17}}{17}$$
2. $$4\sqrt{3}$$
3. $$\frac{6\sqrt{5}}{7}$$
4. $$\frac{a^2\sqrt{a}}{b}$$
5. $$\sqrt{x-3}$$
6. $$\frac{\sqrt{26}+1}{25}$$
7. $$\sqrt{37}-\sqrt{2}$$
8. $$\frac{\sqrt{47}+\sqrt{15}}{2}$$
9. $$\sqrt{x+5}+3$$
10. $$x(\sqrt{x+8}+2)$$
11. $$-(x+4)(3+\sqrt{x+5})$$
12. $$\frac{\sqrt{3+2x}-\sqrt{3-x}}{3}$$