Question

Выполните действия:

1) (3√2 + 2√7) · √2 - √56

2) (√7 - 3)(3 + √7)

3) (3√2 + 1)² - 2√18

Сократите дробь:

x - 4
₋₋₋₋₋₋₋₋₋₋₋₋₋₋
x - 2√x

Answer 1

$1)(3\sqrt{2}+2\sqrt{7})*\sqrt{2}-\sqrt{56}=3\sqrt{2}*\sqrt{2} +2\sqrt{7}*\sqrt{2}-\sqrt{4*14}=6+2\sqrt{14}-2\sqrt{14}=6\\\\2)(\sqrt{7}-3)(3+\sqrt{7})=(\sqrt{7})^{2}-3^{2}=7-9=-2$

$3)(3\sqrt{2}+1)^{2} -2\sqrt{18}=(3\sqrt{2})^{2}+2*3\sqrt{2}*1+1^{2}-2\sqrt{9*2}=18+6\sqrt{2}+1-6\sqrt{2}=19\\\\4)\frac{x-4}{x-2\sqrt{x} }=\frac{(\sqrt{x})^{2}-2^{2}}{(\sqrt{x})^{2}-2\sqrt{x}}=\frac{(\sqrt{x}-2)(\sqrt{x}+2)}{\sqrt{x}(\sqrt{x}-2)}=\frac{\sqrt{x}+2 }{\sqrt{x} }$