Question

Решить уравнение во вложении

Answer 1

$x^6=frac{257x^2-68}{68x^2-257}; x^2=tge 0; t^3=frac{257t-68}{68t-257}; tnot= frac{257}{68}; t^3(68t-257)=257t-68;$

$68t^4-257t^3-257t+68=0; tnot= 0; 68(t^2+frac{1}{t^2})-257(t+frac{1}{t})=0; t+frac{1}{t}=p>0;$

$68(p^2-2)-257p=0; 68p^2-257p-136=0; D=257^2-4cdot 68cdot (-136)=321^2;$

$p=frac{257pm 321}{2cdot 68}=left [ {{17/4} atop {-8/17<0}} right. ; t+frac{1}{t}=frac{17}{4}; left [ {{t=4} atop {t=1/4}} right. ; left [ {{x=pm 2} atop {x=pm 1/2}} right.$

Ответ: $pm 2; pmfrac{1}{2}$