Упр.89 ГДЗ Колягин Ткачёва 9 класс (Алгебра)

1) ((125x)^(1/3)-(8x)^(1/3))-((27x)^(1/3)-(64x)^(1/3));
2) (x^(1/4)+(16x)^(1/4))+((81x)^(1/4)-(625x)^(1/4));
3) (3/v(1+a)+v(1-a)):(3+v(1-a^2))/v(1+a);
4) (1-x/v(x^2-y^2)):(v(x^2-y^2)-x).

1. $$\left(\sqrt[3]{125x}-\sqrt[3]{8x}\right)-\left(\sqrt[3]{27x}-\sqrt[3]{64x}\right)$$

   $$=\left(5\sqrt[3]{x}-2\sqrt[3]{x}\right)-\left(3\sqrt[3]{x}-4\sqrt[3]{x}\right)$$

   $$=3\sqrt[3]{x}-\left(-\sqrt[3]{x}\right)=4\sqrt[3]{x}$$

2. $$\left(\sqrt[4]{x}+\sqrt[4]{16x}\right)+\left(\sqrt[4]{81x}-\sqrt[4]{625x}\right)$$

   $$=\left(\sqrt[4]{x}+2\sqrt[4]{x}\right)+\left(3\sqrt[4]{x}-5\sqrt[4]{x}\right)$$

   $$=3\sqrt[4]{x}-2\sqrt[4]{x}=\sqrt[4]{x}$$

3. $$\left(\frac{3}{\sqrt{1+a}}+\sqrt{1-a}\right):\frac{3+\sqrt{1-a^2}}{\sqrt{1+a}}$$

   $$=\frac{3+\sqrt{(1-a)(1+a)}}{\sqrt{1+a}}\cdot\frac{\sqrt{1+a}}{3+\sqrt{1-a^2}}$$

   $$=\frac{3+\sqrt{1-a^2}}{3+\sqrt{1-a^2}}=1$$

4. $$\left(1-\frac{x}{\sqrt{x^2-y^2}}\right):\left(\sqrt{x^2-y^2}-x\right)$$

   $$=\frac{\sqrt{x^2-y^2}-x}{\sqrt{x^2-y^2}}:\left(\sqrt{x^2-y^2}-x\right)$$

   $$=\frac{1}{\sqrt{x^2-y^2}}$$

Ответ

1) $$4\sqrt[3]{x}$$;
2) $$\sqrt[4]{x}$$;
3) $$1$$;
4) $$\frac{1}{\sqrt{x^2-y^2}}$$.