(x/x-1)^2+(x/x+1)^2=10/9

Question

(x/x-1)^2+(x/x+1)^2=10/9

Answer 1

(x/(x-1))^2+(x/(x+1))^2=10/9

x²/(x-1)²+x²/(x+1)²=10/9

x²((x+1)²+(x-1)²)/((x-1)²(x+1)²)=10/9
x²((x²+2x+1)+(x²-2x+1))/((x²-1)²)=10/9

x²((x²+1)+(x²+1))/((x²-1)²)=10/9
2x²(x²+1)·9=10(x²-1)²
9x⁴+9x²=5x⁴-10x²+5  

 4x⁴+19x²-5 =0    

t=x²≥0   4t²+19t-5 =0 

D=19²+4·4·5=361+80=441=21²
t1=(-19-21)/8 <0 - посторонний корень<br>t2=(-19+21)/8 =1/4     x²=1/4   x1=1/2    x2=-1/2