Question

Как решить, помогите пжлст( желательно с пояснениями

Answer 1

1) $x^2-(sqrt{5} +sqrt{3} )x+sqrt{15}$

$D=b^2-4ac=(sqrt{5} +sqrt{3})^2-4sqrt{15} =(sqrt{5})^2+2sqrt{15} +(sqrt{3})^2-4sqrt{15} =\ =(sqrt{5}-sqrt{3})^2\ Rightarrow sqrt{D} =sqrt{(sqrt{5}-sqrt{3})^2} =|sqrt{5}-sqrt{3}|=sqrt{5}-sqrt{3};\ x=dfrac{(sqrt{5}+sqrt{3})б(sqrt{5}-sqrt{3})}{2};\ x_1=sqrt{3}; x_2=sqrt{5}.$

2) $x^2+(sqrt{7} -sqrt{5})x-sqrt{35}$

$D=b^2-4ac=(sqrt{7} -sqrt{5})^2+4sqrt{35} =(sqrt{7})^2-2sqrt{35} +(sqrt{5})^2+4sqrt{35} =\ =(sqrt{7}+sqrt{5})^2\ Rightarrow sqrt{D} =sqrt{(sqrt{7}+sqrt{5})^2} =|sqrt{7}+sqrt{5}|=sqrt{7}+sqrt{5};\ x=dfrac{(sqrt{5}-sqrt{7})б(sqrt{7}+sqrt{5})}{2};\ x_1=-sqrt{7}; x_2=sqrt{5}.$

3) $dfrac{x^2-(sqrt{5} +sqrt{3} )x+sqrt{15}}{x^2+(sqrt{7} -sqrt{5})x-sqrt{35}}=dfrac{(x-sqrt{3})(x-sqrt{5})}{(x+sqrt{7})(x-sqrt{5})}=dfrac{x-sqrt{3}}{x+sqrt{7}}.$

Ответ: $dfrac{x-sqrt{3}}{x+sqrt{7}}$