Question

Помогите кто чем может !!!!

Answer 1

$1);a);frac{sqrt{-125}}{sqrt{-5}}cdotsqrt[3]8=sqrt{frac{-125}{-5}}cdotsqrt[3]{2^3}=sqrt{25}cdot2=5cdot2=10$
$b);frac{(sqrt[4]{24}+sqrt[4]6)^2}{4sqrt3+3sqrt6}=frac{sqrt[4]{24}cdotsqrt[4]{24}+sqrt[4]{6}cdotsqrt[4]{24}+sqrt[4]{6}cdotsqrt[4]{24}+sqrt[4]{6}cdotsqrt[4]{6}}{4sqrt3+3sqrt6}=frac{sqrt[4]{24cdot24}+2sqrt[4]{6cdot24}+sqrt[4]{6cdot6}}{4sqrt3+3sqrt6}=frac{sqrt{24}+2sqrt[4]{144}+sqrt{6}}{4sqrt3+3sqrt6}=\=frac{sqrt{4cdot6}+2sqrt{12}+sqrt6}{4sqrt3+3sqrt6}=frac{2sqrt6+4sqrt3+sqrt6}{4sqrt3+3sqrt6}=frac{4sqrt3+3sqrt6}{4sqrt3+3sqrt6}=1$
$2.;a);frac{c+c^frac12cdot d^frac12+d}{c^frac32-d^frac32}=frac{c+c^frac12cdot d^frac12+d}{(c^frac12-d^frac12)(c+c^frac12cdot d^frac12+d)}=frac1{c^frac12-d^frac12}$
$b);frac{a-b}{a^frac12-b^frac12}-frac{a^frac32-b^frac32}{a-b}=frac{a-b}{a^frac12-b^frac12}-frac{a^frac32-b^frac32}{(a^frac12-b^frac12)(a^frac12+b^frac12)}=frac{(a^frac12+b^frac12)(a-b)-(a^frac32-b^frac32)}{{(a^frac12-b^frac12)(a^frac12+b^frac12)}}=$
$=frac{a^frac32-a^frac12b+ab^frac12-b^frac32-a^frac32+b^frac32}{{(a^frac12-b^frac12)(a^frac12+b^frac12)}}=frac{ab^frac12-a^frac12b}{{(a^frac12-b^frac12)(a^frac12+b^frac12)}}=frac{a^frac12b^frac12(a^frac12-b^frac12)}{{(a^frac12-b^frac12)(a^frac12+b^frac12)}}=frac{a^frac12b^frac12}{(a^frac12+b^frac12)}$