Question

Решите пожалуйста

Номера 517, 522, 524(а,б)

Answer 1

$sqrt{ frac{1,69a^8}{b^2} } ,b textless 0$
$frac{sqrt{1,69a^8}}{sqrt{b^2}}= frac{sqrt{13^2*(a^4)^2}}{|b|}= frac{|13|*|a^4|}{|b|}= frac{13a^4}{-b}= -frac{13a^4}{b};$
$sqrt{ frac{0,16a^{14}}{b^{12}} }= frac{ sqrt{0,16a^{14}} }{ sqrt{b^{12}} }= frac{sqrt{(0,4)^2*(a^7)^2}}{sqrt{(b^6)^2}}= frac{|0,4|*|a^7|}{|b^6|}= frac{0,4a^7}{b^6} ,a textgreater 0.$
$(sqrt{ab}-sqrt{ frac{b}{a} }-sqrt{ frac{a}{b} }+sqrt{ frac{1}{ab} })sqrt{ab}=(a-1)(b-1)$
$(sqrt{ab}- frac{sqrt{b}}{sqrt{a}}- frac{sqrt{a}}{sqrt{b}}+ frac{sqrt{1}}{sqrt{ab}})sqrt{ab}=(a-1)(b-1)$
$( frac{(sqrt{ab}^2-(sqrt{b})^2-(sqrt{a})^2+1)}{sqrt{ab}} )sqrt{ab}=(a-1)(b-1)$
$( frac{ab-b-a+1}{sqrt{ab}})sqrt{ab}=(a-1)(b-1)$
$ab-b-a+1=(a-1)(b-1)$
$ab-b-a+1=ab-a-b+1;$

$frac{2asqrt{ab}+a^2sqrt{b}+2bsqrt{ab}+absqrt{b}}{2sqrt{ab}+asqrt{b}}=a+b$
$frac{2sqrt{ab}(a+b)+asqrt{b}(a+b)}{2sqrt{ab}+asqrt{b}}=a+b$
$frac{(a+b)(2sqrt{ab}+asqrt{b})}{(2sqrt{ab}+asqrt{b})}=a+b$
$a+b=a+b$

$(sqrt{6x}-2)^2=sqrt{3}(sqrt{2x}-sqrt{12})+6x$
$6x-4sqrt{6x}+4=sqrt{6x}-6+6x$
$6x-6x-4sqrt{6x}-sqrt{6x}=-6-4$
$-5sqrt{6x}=-10$
$sqrt{6x}=2$
$(sqrt{6x})^2=2^2$
$6x=4$
$x= frac{4}{6}= frac{2}{3}$

$(sqrt{7x}-2sqrt{5})(sqrt{7x}+2sqrt{5})=7x-sqrt{2}(sqrt{5x}-sqrt{72})$
$(sqrt{7x})^2-(2sqrt{5})^2=7x-sqrt{10x}+sqrt{144}$
$7x-10=7x-sqrt{10x}+12$
$7x-7x+sqrt{10x}=12+10$
$sqrt{10x}=22$
$(sqrt{10x})^2=22^2$
$10x=484$
$x=48,4$

Answer 2

Если решу уравнения, обновлю ответ.

Answer 3

Ок

Answer 4

Спс