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

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

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