1)
8/(y¹/⁴+2)+(y-8y¹/⁴)/(y¹/²-4) y=25
Пусть y¹/⁴=t ⇒
8/(t+2)+(t⁴-8t)/(t²-4)-8/(t+2)+(t⁴-8t)/((t+2)(t-2))=(8*(t-2)+t⁴-8t)/((t-2)(t+2))=
=(8t-16+t⁴-8t)/((t²-4)=(t⁴-16)/(t²-4)=(t²-4)(t²+4)/(t²-4)=t²+4=(y¹/⁴)²+4=
=y¹/²+4=√25+4=5+4=9.
2)
((a-b)/(a¹/⁴*b¹/²-b³/⁴))*(b⁰,⁷⁵/((a¹/²+b¹/²)*(a¹/⁴*b¹/⁴+b¹/²))
Пусть a¹/⁴=t, b¹/⁴=v ⇒
((t⁴-v⁴)/(t*v²-v³))*(v³/((t²+v²)*(t*v+v²))=(t²-v²)(t²+v²)*v³/(v²*(t-v)*(t²+v²)*v*(t+v))=
=v³*(t²-v²)*(t²+v²)/((v³*(t²-v²)*(t²+v²))=1.