The equation can be recast as (33+1/x^2)^1/4 +(49-1/x^2)^1/4=4. Let (33+1/x^2)^1/4 =a and (49-1/x^2)^1/4 =b. So, a+b=4 and a^4 +b^4 = 82. Let ab=t. Then we get t^2-32t+87 =0. So, t=ab=3,29. t =29 does not yield real x. For t=3, a=1,3. a=1 does not yield real x. For a=3, x=+/-1/(4√3).
The equation can be recast as (33+1/x^2)^1/4 +(49-1/x^2)^1/4=4. Let (33+1/x^2)^1/4 =a and (49-1/x^2)^1/4 =b. So, a+b=4 and a^4 +b^4 = 82. Let ab=t. Then we get t^2-32t+87 =0. So, t=ab=3,29. t =29 does not yield real x. For t=3, a=1,3. a=1 does not yield real x. For a=3, x=+/-1/(4√3).
something wrong
X=+-1/ 4 root3
u+v=4; u^4+v^4=82; =>
u+v=1+3 or 3+1; &
u^4+v^4=82=1^4+3^4; or3^4+1^4=>3; u=1 or 3;
u^4=1 or 81=,,33+a^2;
=33+1/x^2;=> x^2=1/-32 or 1/48; x=±1/4√3 ;
X=+-sqr3/12
Τελικα 1/χ^2=48 χ^2=1/48 χ=+ -(3)^(1/2)/12.
x=+-1/4√3